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Mathematics LibreTexts

5.2.1: Solving Percent Problems

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Learning Objectives

  • Identify the amount, the base, and the percent in a percent problem.
  • Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100, so they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

  • The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.
  • The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.
  • The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price.

You will return to this problem a bit later. The following examples show how to identify the three parts: the percent, the base, and the amount.

Identify the percent, amount, and base in this problem.

30 is 20% of what number?

Percent: The percent is the number with the % symbol: 20%.

Base : The base is the whole amount, which in this case is unknown.

Amount: The amount based on the percent is 30.

Percent=20%

Base=unknown

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Identify the percent, base, and amount in this problem:

What percent of 30 is 3?

The percent is unknown, because the problem states " What percent?" The base is the whole in the situation, so the base is 30. The amount is the portion of the whole, which is 3 in this case.

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (=) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

\[\ \text { Percent } {\color{red}\cdot}\text { Base }{\color{blue}=}\text { Amount } \nonumber \]

In the examples below, the unknown is represented by the letter \(\ n\). The unknown can be represented by any letter or a box \(\ \square\) or even a question mark.

Write an equation that represents the following problem.

\(\ 20 \% \cdot n=30\)

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as \(\ 20 \% \cdot n=30\), you can divide 30 by 20% to find the unknown: \(\ n=30 \div 20 \%\).

You can solve this by writing the percent as a decimal or fraction and then dividing.

\(\ n=30 \div 20 \%=30 \div 0.20=150\)

What percent of 72 is 9?

\(\ 12.5 \% \text { of } 72 \text { is } 9\).

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

\(\ 10 \% \text { of } 72=0.1 \cdot 72=7.2\)

\(\ 20 \% \text { of } 72=0.2 \cdot 72=14.4\)

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

What is 110% of 24?

\(\ 26.4 \text { is } 110 \% \text { of } 24\).

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

18 is what percent of 48?

  • \(\ 0.375 \%\)
  • \(\ 8.64 \%\)
  • \(\ 37.5 \%\)
  • \(\ 864 \%\)

Incorrect. You may have calculated properly, but you forgot to move the decimal point when you rewrote your answer as a percent. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Incorrect. You may have used \(\ 18\) or \(\ 48\) as the percent, rather than the amount or base. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Correct. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives \(\ 37.5 \%\).

Incorrect. You probably used 18 or 48 as the percent, rather than the amount or base, and also forgot to rewrite the percent as a decimal before multiplying. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Using Proportions to Solve Percent Problems

Percent problems can also be solved by writing a proportion. A proportion is an equation that sets two ratios or fractions equal to each other. With percent problems, one of the ratios is the percent, written as \(\ \frac{n}{100}\). The other ratio is the amount to the base.

\(\ \text { Percent }=\frac{\text { amount }}{\text { base }}\)

Write a proportion to find the answer to the following question.

30 is 20% of 150.

18 is 125% of what number?

  • \(\ 0.144\)
  • \(\ 694 \frac{4}{9}\) (or about \(\ 694.4\))

Incorrect. You probably didn’t write a proportion and just divided 18 by 125. Or, you incorrectly set up one fraction as \(\ \frac{18}{125}\) and set this equal to the base, \(\ n\). The percent in this case is 125%, so one fraction in the proportion should be \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Correct. The percent in this case is 125%, so one fraction in the proportion should be \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Incorrect. You probably put the amount (18) over 100 in the proportion, rather than the percent (125). Perhaps you thought 18 was the percent and 125 was the base. The correct percent fraction for the proportion is \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Incorrect. You probably confused the amount (18) with the percent (125) when you set up the proportion. The correct percent fraction for the proportion is \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Let’s go back to the problem that was posed at the beginning. You can now solve this problem as shown in the following example.

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off of the $220 original price .

The coupon will take $33 off the original price.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

\(\ \begin{array}{l} 10 \% \text { of } 220=0.1 \cdot 220=22 \\ 20 \% \text { of } 220=0.2 \cdot 220=44 \end{array}\)

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

Evelyn bought some books at the local bookstore. Her total bill was $31.50, which included 5% tax. How much did the books cost before tax?

The books cost $30 before tax.

Susana worked 20 hours at her job last week. This week, she worked 35 hours. In terms of a percent, how much more did she work this week than last week?

Since 35 is 175% of 20, Susana worked 75% more this week than she did last week. (You can think of this as, “Susana worked 100% of the hours she worked last week, as well as 75% more.”)

Percent problems have three parts: the percent, the base (or whole), and the amount. Any of those parts may be the unknown value to be found. To solve percent problems, you can use the equation, \(\ \text { Percent } \cdot \text { Base }=\text { Amount }\), and solve for the unknown numbers. Or, you can set up the proportion, \(\ \text { Percent }=\frac{\text { amount }}{\text { base }}\), where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.

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How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

How to Solve Percent Problems? (+FREE Worksheet!)

Related Topics

  • How to Find Percent of Increase and Decrease
  • How to Find Discount, Tax, and Tip
  • How to Do Percentage Calculations
  • How to Solve Simple Interest Problems

Step by step guide to solve percent problems

  • In each percent problem, we are looking for the base, or part or the percent.
  • Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

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Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

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Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

  • \(51\) is \(340\%\) of what?
  • \(93\%\) of what number is \(97\)?
  • \(27\%\) of \(142\) is what number?
  • What percent of \(125\) is \(29.3\)?
  • \(60\) is what percent of \(126\)?
  • \(67\) is \(67\%\) of what?

Download Percent Problems Worksheet

  • \(\color{blue}{15}\)
  • \(\color{blue}{104.3}\)
  • \(\color{blue}{38.34}\)
  • \(\color{blue}{23.44\%}\)
  • \(\color{blue}{47.6\%}\)
  • \(\color{blue}{100}\)

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Solving problems with percentages

  • Price difference I
  • Price difference II
  • How many students?

To solve problems with percent we use the percent proportion shown in "Proportions and percent".

$$\frac{a}{b}=\frac{x}{100}$$

$$\frac{a}{{\color{red} {b}}}\cdot {\color{red} {b}}=\frac{x}{100}\cdot b$$

$$a=\frac{x}{100}\cdot b$$

x/100 is called the rate.

$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$

Where the base is the original value and the percentage is the new value.

47% of the students in a class of 34 students has glasses or contacts. How many students in the class have either glasses or contacts?

$$a=r\cdot b$$

$$47\%=0.47a$$

$$=0.47\cdot 34$$

$$a=15.98\approx 16$$

16 of the students wear either glasses or contacts.

We often get reports about how much something has increased or decreased as a percent of change. The percent of change tells us how much something has changed in comparison to the original number. There are two different methods that we can use to find the percent of change.

The Mathplanet school has increased its student body from 150 students to 240 from last year. How big is the increase in percent?

We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.

$$240-150=90$$

Then we find out how many percent this change corresponds to when compared to the original number of students

$$90=r\cdot 150$$

$$\frac{90}{150}=r$$

$$0.6=r= 60\%$$

We begin by finding the ratio between the old value (the original value) and the new value

$$percent\:of\:change=\frac{new\:value}{old\:value}=\frac{240}{150}=1.6$$

As you might remember 100% = 1. Since we have a percent of change that is bigger than 1 we know that we have an increase. To find out how big of an increase we've got we subtract 1 from 1.6.

$$1.6-1=0.6$$

$$0.6=60\%$$

As you can see both methods gave us the same answer which is that the student body has increased by 60%

Video lessons

A skirt cost $35 regulary in a shop. At a sale the price of the skirtreduces with 30%. How much will the skirt cost after the discount?

Solve "54 is 25% of what number?"

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Solving Percent Problems

Learning Objective(s)

·          Identify the amount, the base, and the percent in a percent problem.

·          Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100. So they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.

The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.

The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price .

You will return to this problem a bit later. The following examples show how to identify the three parts, the percent, the base, and the amount.

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (= ) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

Percent · Base = Amount

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as 20% · n = 30, you can divide 30 by 20% to find the unknown: n =  30 ÷ 20%.

You can solve this by writing the percent as a decimal or fraction and then dividing.

n = 30 ÷ 20% =  30 ÷ 0.20 = 150

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

10% of 72 = 0.1 · 72 = 7.2

20% of 72 = 0.2 · 72 = 14.4

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

Using Proportions to Solve Percent Problems

Let’s go back to the problem that was posed at the beginning. You can now solve this problem as shown in the following example.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

10% of 220 = 0.1 · 220 = 22

20% of 220 = 0.2 · 220 = 44

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

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Unit 3: Fractions, decimals, & percentages

About this unit, converting fractions to decimals.

  • Rewriting decimals as fractions: 2.75 (Opens a modal)
  • Worked example: Converting a fraction (7/8) to a decimal (Opens a modal)
  • Fraction to decimal: 11/25 (Opens a modal)
  • Fraction to decimal with rounding (Opens a modal)
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Adding & subtracting rational numbers

  • Comparing rational numbers (Opens a modal)
  • Adding & subtracting rational numbers: 79% - 79.1 - 58 1/10 (Opens a modal)
  • Adding & subtracting rational numbers: 0.79 - 4/3 - 1/2 + 150% (Opens a modal)
  • Order rational numbers Get 3 of 4 questions to level up!
  • Adding & subtracting rational numbers Get 3 of 4 questions to level up!

Percent word problems

  • Solving percent problems (Opens a modal)
  • Percent word problem: magic club (Opens a modal)
  • Percent word problems: tax and discount (Opens a modal)
  • Percent word problem: guavas (Opens a modal)
  • Equivalent expressions with percent problems Get 3 of 4 questions to level up!
  • Percent problems Get 3 of 4 questions to level up!
  • Tax and tip word problems Get 3 of 4 questions to level up!
  • Discount, markup, and commission word problems Get 3 of 4 questions to level up!

Rational number word problems

  • Rational number word problem: school report (Opens a modal)
  • Rational number word problem: cosmetics (Opens a modal)
  • Rational number word problem: cab (Opens a modal)
  • Rational number word problem: ice (Opens a modal)
  • Rational number word problem: computers (Opens a modal)
  • Rational number word problem: stock (Opens a modal)
  • Rational number word problem: checking account (Opens a modal)
  • Rational number word problems Get 3 of 4 questions to level up!

Percentages Worksheets

Welcome to the percentages math worksheet page where we are 100% committed to providing excellent math worksheets. This page includes Percentages worksheets including calculating percentages of a number, percentage rates, and original amounts and percentage increase and decrease worksheets.

As you probably know, percentages are a special kind of decimal. Most calculations involving percentages involve using the percentage in its decimal form. This is achieved by dividing the percentage amount by 100. There are many worksheets on percentages below. In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate.

Most Popular Percentages Worksheets this Week

Calculating the Percent Value of Whole Number Amounts and All Percents

Percentage Calculations

problem solving involving percentages

Calculating the percentage value of a number involves a little bit of multiplication. One should be familiar with decimal multiplication and decimal place value before working with percentage values. The percentage value needs to be converted to a decimal by dividing by 100. 18%, for example is 18 ÷ 100 = 0.18. When a question asks for a percentage value of a number, it is asking you to multiply the two numbers together.

Example question: What is 18% of 2800? Answer: Convert 18% to a decimal and multiply by 2800. 2800 × 0.18 = 504. 504 is 18% of 2800.

  • Calculating the Percentage Value (Whole Number Results) Calculating the Percentage Value (Whole Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Number Results) (Select percents) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 25%)
  • Calculating the Percentage Value (Decimal Number Results) Calculating the Percentage Value (Decimal Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Number Results) (Select percents) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 25%)
  • Calculating the Percentage Value (Whole Dollar Results) Calculating the Percentage Value (Whole Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Dollar Results) (Select percents) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 25%)
  • Calculating the Percentage Value (Decimal Dollar Results) Calculating the Percentage Value (Decimal Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Dollar Results) (Select percents) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 25%)

Calculating what percentage one number is of another number is the second common type of percentage calculation. In this case, division is required followed by converting the decimal to a percentage. If the first number is 100% of the value, the second number will also be 100% if the two numbers are equal; however, this isn't usually the case. If the second number is less than the first number, the second number is less than 100%. If the second number is greater than the first number, the second number is greater than 100%. A simple example is: What percentage of 10 is 6? Because 6 is less than 10, it must also be less than 100% of 10. To calculate, divide 6 by 10 to get 0.6; then convert 0.6 to a percentage by multiplying by 100. 0.6 × 100 = 60%. Therefore, 6 is 60% of 10.

Example question: What percentage of 3700 is 2479? First, recognize that 2479 is less than 3700, so the percentage value must also be less than 100%. Divide 2479 by 3700 and multiply by 100. 2479 ÷ 3700 × 100 = 67%.

  • Calculating the Percentage a Whole Number is of Another Whole Number Calculating the Percentage a Whole Number is of Another Whole Number (Percents from 1% to 99%) Calculating the Percentage a Whole Number is of Another Whole Number (Select percents) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 25%)
  • Calculating the Percentage a Decimal Number is of a Whole Number Calculating the Percentage a Decimal Number is of a Whole Number (Percents from 1% to 99%) Calculating the Percentage a Decimal Number is of a Whole Number (Select percents) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 25%)
  • Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Select percents) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 25%)
  • Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Select percents) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 25%)

The third type of percentage calculation involves calculating the original amount from the percentage value and the percentage. The process involved here is the reverse of calculating the percentage value of a number. To get 10% of 100, for example, multiply 100 × 0.10 = 10. To reverse this process, divide 10 by 0.10 to get 100. 10 ÷ 0.10 = 100.

Example question: 4066 is 95% of what original amount? To calculate 4066 in the first place, a number was multiplied by 0.95 to get 4066. To reverse this process, divide to get the original number. In this case, 4066 ÷ 0.95 = 4280.

  • Calculating the Original Amount from a Whole Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Whole Numbers ) Calculating the Original Amount (Select percents) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Whole Numbers )
  • Calculating the Original Amount from a Decimal Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Decimals ) Calculating the Original Amount (Select percents) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Decimals )
  • Calculating the Original Amount from a Whole Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
  • Calculating the Original Amount from a Decimal Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )
  • Mixed Percentage Calculations with Whole Number Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Whole Numbers )
  • Mixed Percentage Calculations with Decimal Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Decimals ) Mixed Percentage Calculations (Select percents) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Decimals )
  • Mixed Percentage Calculations with Whole Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
  • Mixed Percentage Calculations with Decimal Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )

Percentage Increase/Decrease Worksheets

problem solving involving percentages

The worksheets in this section have students determine by what percentage something increases or decreases. Each question includes an original amount and a new amount. Students determine the change from the original to the new amount using a formula: ((new - original)/original) × 100 or another method. It should be straight-forward to determine if there is an increase or a decrease. In the case of a decrease, the percentage change (using the formula) will be negative.

  • Percentage Increase/Decrease With Whole Number Percentage Values Percentage Increase/Decrease Whole Numbers with 1% Intervals Percentage Increase/Decrease Whole Numbers with 5% Intervals Percentage Increase/Decrease Whole Numbers with 25% Intervals
  • Percentage Increase/Decrease With Decimal Number Percentage Values Percentage Increase/Decrease Decimals with 1% Intervals Percentage Increase/Decrease Decimals with 5% Intervals Percentage Increase/Decrease Decimals with 25% Intervals
  • Percentage Increase/Decrease With Whole Dollar Percentage Values Percentage Increase/Decrease Whole Dollar Amounts with 1% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 5% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 25% Intervals
  • Percentage Increase/Decrease With Decimal Dollar Percentage Values Percentage Increase/Decrease Decimal Dollar Amounts with 1% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 5% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 25% Intervals

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Enter the value(s) for the required question and click the adjacent Go button.

PERCENTAGES

This section will explain how to apply algebra to percentage problems.

In algebra problems, percentages are usually written as decimals.

Example 1. Ethan got 80% of the questions correct on a test, and there were 55 questions. How many did he get right?

The number of questions correct is indicated by:

problem solving involving percentages

Ethan got 44 questions correct.

Explanation: % means "per one hundred". So 80% means 80/100 = 0.80.

Example 2. A math teacher, Dr. Pi, computes a student’s grade for the course as follows:

problem solving involving percentages

a. Compute Darrel's grade for the course if he has a 91 on the homework, 84 for his test average, and a 98 on the final exam.

problem solving involving percentages

Darrel’s grade for the course is an 89.6, or a B+.

b. Suppose Selena has an 89 homework average and a 97 test average. What does Selena have to get on the final exam to get a 90 for the course?

The difference between Part a and Part b is that in Part b we don’t know Selena’s grade on the final exam.

So instead of multiplying 30% times a number, multiply 30% times E. E is the variable that represents what Selena has to get on the final exam to get a 90 for the course.

problem solving involving percentages

Because Selena studied all semester, she only has to get a 79 on the final to get a 90 for the course.

Example 3. Sink Hardware store is having a 15% off sale. The sale price of a toilet is $97; find the retail price of the toilet.

a. Complete the table to find an equation relating the sale price to the retail price (the price before the sale).

Vocabulary: Retail price is the original price to the consumer or the price before the sale. Discount is how much the consumer saves, usually a percentage of the retail price. Sale Price is the retail price minus the discount.

problem solving involving percentages

b. Simplify the equation.

problem solving involving percentages

Explanation: The coefficient of R is one, so the arithmetic for combining like terms is 1 - 0.15 = .85. In other words, the sale price is 85% of the retail price.

c. Solve the equation when the sale price is $97.

problem solving involving percentages

The retail price for the toilet was $114.12. (Note: the answer was rounded to the nearest cent.)

The following diagram is meant as a visualization of problem 3.

problem solving involving percentages

The large rectangle represents the retail price. The retail price has two components, the sale price and the discount. So Retail Price = Sale Price + Discount If Discount is subtracted from both sides of the equation, a formula for Sale Price is found. Sale Price = Retail Price - Discount

Percentages play an integral role in our everyday lives, including computing discounts, calculating mortgages, savings, investments, and estimating final grades. When working with percentages, remember to write them as decimals, to create tables to derive equations, and to follow the proper procedures to solve equations.

Study Tip: Remember to use descriptive letters to describe the variables.

CHAPTER 1 REVIEW

This unit introduces algebra by examining similar models. You should be able to read a problem and create a table to find an equation that relates two variables. If you are given information about one of the variables, you should be able to use algebra to find the other variable.

Signed Numbers:

Informal Rules:

Adding or subtracting like signs: Add the two numbers and use the common sign.

problem solving involving percentages

Adding or subtracting unlike signs: Subtract the two numbers and use the sign of the larger, (more precisely, the sign of the number whose absolute value is largest.)

problem solving involving percentages

Multiplying or dividing like signs: The product or quotient of two numbers with like signs is always positive.

problem solving involving percentages

Multiplying or dividing unlike signs: The product or quotient of two numbers with unlike signs is always negative.

problem solving involving percentages

Order of operations: P lease E xcuse M y D ear A unt S ally 1. Inside P arentheses, (). 2. E xponents. 3. M ultiplication and D ivision (left to right) 4. A ddition and S ubtraction (left to right)

problem solving involving percentages

Study Tip: All of these informal rules should be written on note cards.

Introduction to Variables:

Generate a table to find an equation that relates two variables.

Example 6. A car company charges $14.95 plus 35 cents per mile.

problem solving involving percentages

Simplifying Algebraic Equations:

problem solving involving percentages

Combine like terms:

problem solving involving percentages

Solving Equations:

1. Simplify both sides of the equation. 2. Write the equation as a variable term equal to a constant. 3. Divide both sides by the coefficient or multiply by the reciprocal. 4. Three possible outcomes to solving an equation. a. One solution ( a conditional equation ) b. No solution ( a contradiction ) c. Every number is a solution (an identity )

problem solving involving percentages

Applications of Linear Equations:

This section summarizes the major skills taught in this chapter.

Example 9. A cell phone company charges $12.50 plus 15 cents per minute after the first six minutes.

a. Create a table to find the equation that relates cost and minutes.

problem solving involving percentages

c. If the call costs $23.50, how long were you on the phone?

problem solving involving percentages

If the call costs $23.50, then you were on the phone for approximately 79 minutes.

Literal Equations:

A literal equation involves solving an equation for one of two variables.

problem solving involving percentages

Percentages:

Write percentages as decimals.

Example 11. An English teacher computes his grades as follows:

problem solving involving percentages

Sue has an 87 on the short essays and a 72 on the research paper. If she wants an 80 for the course, what grade does Sue have to get on the final?

problem solving involving percentages

Sue has to get a 78.36 in the final exam to get an 80 for the course.

Study Tips:

1. Make sure you have done all of the homework exercises. 2. Practice the review test on the following pages by placing yourself under realistic exam conditions. 3. Find a quiet place and use a timer to simulate the test period. 4. Write your answers in your homework notebook. Make copies of the exam so you may then re-take it for extra practice. 5. Check your answers. 6. There is an additional exam available on the Beginning Algebra web page. 7. DO NOT wait until the night before the exam to study.

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Fractions, Decimals and Percentages - Short Problems

problem solving involving percentages

Talulah's Tulips

Weekly Problem 10 - 2017 Talulah plants some tulip bulbs. When they flower, she notices something interesting about the colours. What fraction of the tulips are white?

Smashing Time

Weekly Problem 58 - 2012 Once granny has smashed some of her cups and saucers, how many cups are now without saucers?

Better Spelling

Weekly Problem 12 - 2010 Can Emily increase her average test score to more than $80$%? Find out how many more tests she must take to do so.

Valuable Percentages

Weekly Problem 23 - 2010 These numbers have been written as percentages. Can you work out which has the greatest value?

Bouncing Ball

A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell.

Percentage Mad

Weekly Problem 43 - 2013 What is 20% of 30% of 40% of £50?

Information Display

The information display on a train shows letters by illuminating dots in a rectangular array. What fraction of the dots in this array is illuminated?

Mean Sequence

Weekly Problem 38 - 2009 This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?

Ordering Fractions

Weekly Problem 46 - 2014 Which of these fractions has greatest value?

Jacob's Flock

How many sheep are in Jacob's flock?

Tommy's Tankard

Weekly Problem 4 - 2017 Tommy's tankard holds 480ml when it is one quarter empty. How much does it hold when it is one quarter full?

Farthest Fraction

Which of these fractions is the largest?

Multiplication Magic Square

Weekly Problem 32 - 2015 Can you work out the missing numbers in this multiplication magic square?

Magical Products

Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?

Smallest Fraction

Which of these is the smallest?

Three Blind Mice

Each of the three blind mice in turn ate a third of what remained of a piece of cheese. What fraction of the cheese did they eat in total?

Charlie's Money

How much money did Charlie have to begin with?

Can you find a number that is halfway between two fractions?

Pride of Place

Two fractions have been placed on a number line. Where should another fraction be placed?

Second Half Score

Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?

Between a Sixth and a Twelfth

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

Tricky Fractions

Use this series of fractions to find the value of x.

Too Close to Call

Weekly Problem 24 - 2012 Can you put these very close fractions into order?

Slightly Outnumbered

If this class contains between $45$% and $50$% girls, what is the smallest possible number of girls in the class?

What fraction of this triangle is shaded?

Peanut Harvest

A group of monkeys eat various fractions of a harvest of peanuts. What fraction is left behind?

A Drink of Water

Weekly Problem 43 - 2015 Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?

Entrance Exam

Dean finishes his exam strongly. Can you work out how many questions are on the paper if he gets an average of 80%?

Which of the cities shown had the largest percentage increase in population?

Test Scores

Ivan, Tibor and Alex sat a test and achieved 85%, 90% and 95% respectively. Tibor scored just one more mark than Ivan. How many marks did Alex get?

The Grand Old Duke of York

What percentage of his 10,000 men did the Grand Old Duke of York have left when he arrived back at the bottom of the hill?

Tennis Club

Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?

Meeting Point

Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?

How many rats did the Pied Piper catch?

To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?

Petrol Station

Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?

Recurring Mean

What is the mean of 1.2 recurring and 2.1 recurring?

Itchy's Fleas

Itchy the dog has a million fleas. How many fleas might his shampoo kill?

Weekly Problem 11 - 2013 A shop has "Everything half price", and then "15% off sale prices". What is the overall reduction in cost?

What percentage of the truck's final mass is coal?

What fraction of customers buy Kleenz after the advertising campaign?

Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?

2011 Digits

Weekly Problem 10 - 2014 What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?

Pineapple Juice

What percentage of this orange drink is juice?

After playing 500 games, my success rate at Solitare is 49%. How many games do I need to win to increase my success rate to 50%?

Percentage of a Quarter

What percentage of a quarter is a fifth?

Fractions of 1000

Find a simple way to compute this long fraction.

Breakfast Time

Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?

Percentage Swap

What is 50% of 2007 plus 2007% of 50?

Antiques Roadshow

Last year, on the television programme Antiques Roadshow... work out the approximate profit.

Squeezed In

Weekly Problem 9 - 2017 What integer x makes x/9 lie between 71/7 and 113/11?

Producing an Integer

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Elephants and Geese

Yesterday, at Ulaanbaatar market, a white elephant cost the same amount as 99 wild geese. How many wild geese cost the same amount as a white elephant today?

The Property Market

A property developer sells two houses, and makes a 20% loss on one and a 20% profit on the other. Overall, did he make a profit or a loss?

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Problems Involving Percentage | Percentage Word Problems with Solutions

The percentage of the whole number is calculated by dividing the value by the total value and then multiply by 100. The percentage is nothing but “per 100”. The students of 5th grade can learn the relationship between fractions and percentages with the help of this article. By learning the concept of percent the students can solve different types of problems. We have shown percentage problems with answers in the below sections so that you can verify if you are stuck at some point in percentage problem-solving.

Percentage = (Value/Total Value) × 100

  • To Convert a Percentage into a Fraction
  • Worksheet on Problems Involving Percentage

Real World Problems Involving Percentage

Learn the concept of percentage in-depth by referring to some of the percentage word problems with solutions.

Example 1. In an exam, Preethi secured 278 marks. If she secured 81% Find the maximum marks? Solution: Given, Total number of marks = 278 Preethi secured marks = 81% Percentage formula = P% × X = Y Where P = 81% Y = 278 Then 81% × X = 278 81/100 × X = 278 X = 278 × 100/81 X = 27800/81 = 343.2 Thus Preethi got 278 marks out of 343.2 marks.

Example 2. A container contains 40% of milk. what quantity of container is required to get 160 l of milk? Solution: Given, Let the container contains a milk = 40% Quality of container is required to get = 160 l Percentage formula = P% × X = Y Where P = 40% Y = 160 Then 40% × X = 160 40/100 × X = 160 X = 160 × 100/40 X = 16000/40 = 400

Example 3. There are 200 students in a class. If 20% are absent on a Saturday. Find the number of students present in the class? Solution: Given, Number of students absent on Saturday = 200 Then 20/100 × 200 = 40 Therefore the number of students present = 200 – 40 = 160 students.

Example 4. A box contains of oranges .6% of them are spoiled and 48 are good. find the total number of oranges in the box. Solution: Given, Let the total number of boxes = m 6% of oranges are spoiled and 48 are good Therefore 6% of m = 48 Percentage formula = P% × X = Y 6/100 × m = 66 Then P = 6/100 X = m Y = 66 m = 66 × 100/6 m = 6600/6 = 1100

Example 5. Find the decimal 0.6 into a percentage? Solution: Given, First, we convert the decimal number into a fraction 0.6 = 6/100 = 6% Thus the percentage of the decimal 0.6 is 6%

Example 6. Find the fraction 3/25 into a percentage? Solution: In order to convert the fraction into a percentage, we have to multiply the given fraction by 100. 3/25 × 100 = 12%

Example 7.  Navya scores 68 marks out of 90 in her maths exam. Convert her Marks into percentages? Solution: Given, Navya scores 68 marks out of 90 in her exam 68 × 100/90 = 75% Thus Navya scored 75% on her maths exam.

Example 8. A donkey gives 2l of milk each day. If the milkman sells 50% of the milk, how many litres of milk is left with him Solution: Given, A donkey gives milk = 2l Milk man sells = 50% Percentage formula = P% × X = Y Where P = 50% Y = 2l 50/100 × X = 2 X = 2 × 100/50 X = 200/50 = 4

Example 9. Arjun was able to cover 10% of the 20 km walk in the morning. what is the percentage of the journey is still left to be covered? Solution: Given, Arjun was able to cover 10% of 20 km Percentage formula = P% × X = Y Where P = 10% Y = 20 10/100 × X = 20 X = 20 × 100/10 X = 200/10 = 200

Example 10. In a class 10% of the students are boys. If the total number of students in a class is 80. What is the number of girls? Solution: Given, Total number of boys in a class = 10% Total number of students in a class = 80 Percentage formula = P% × X = Y Where P = 10% Y = 80 10/100 × X = 80 X = 80 × 100/10 X = 800/10 = 80

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Word Problems on Percentage

Word problems on percentage will help us to solve various types of problems related to percentage. Follow the procedure to solve similar type of percent problems.

Word problems on percentage:

1.  In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks.

Let the maximum marks be m.

Ashley’s marks = 83% of m

Ashley secured 332 marks

Therefore, 83% of m = 332

⇒ 83/100 × m = 332

⇒ m = (332 × 100)/83

⇒ m =33200/83

Therefore, Ashley got 332 marks out of 400 marks.

2. An alloy contains 26 % of copper. What quantity of alloy is required to get 260 g of copper?

Let the quantity of alloy required = m g

Then 26 % of m =260 g

⇒ 26/100 × m = 260 g

⇒ m = (260 × 100)/26 g

⇒ m = 26000/26 g

⇒ m = 1000 g

3. There are 50 students in a class. If 14% are absent on a particular day, find the number of students present in the class.

Solution:             

Number of students absent on a particular day = 14 % of 50

                                          i.e., 14/100 × 50 = 7

Therefore, the number of students present = 50 - 7 = 43 students.

4. In a basket of apples, 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket.

Solution:             

Let the total number of apples in the basket be m

12 % of the apples are rotten, and apples in good condition are 66

Therefore, according to the question,

88% of m = 66

⟹ 88/100 × m = 66

⟹ m = (66 × 100)/88

⟹ m = 3 × 25

Therefore, total number of apples in the basket is 75.

5. In an examination, 300 students appeared. Out of these students; 28 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.

The number of students with first division = 28 % of 300

                                                             = 28/100 × 300

                                                             = 8400/100

                                                             = 84

And, the number of students with second division = 54 % of 300

                                                                        = 54/100 × 300

                                                                        =16200/100

                                                                        = 162

Therefore, the number of students who just passed = 300 – (84 + 162)

                                                                           = 54

Questions and Answers on Word Problems on Percentage:

1. In a class 60% of the students are girls. If the total number of students is 30, what is the number of boys?

2. Emma scores 72 marks out of 80 in her English exam. Convert her marks into percent.

Answer: 90%

3. Mason was able to sell 35% of his vegetables before noon. If Mason had 200 kg of vegetables in the morning, how many grams of vegetables was he able to see by noon?

Answer: 70 kg

4. Alexander was able to cover 25% of 150 km journey in the morning. What percent of journey is still left to be covered?

Answer:  112.5 km

5. A cow gives 24 l milk each day. If the milkman sells 75% of the milk, how many liters of milk is left with him?

Answer: 6 l

Word Problems on Percentage

6.  While shopping Grace spent 90% of the money she had. If she had $ 4500 on shopping, what was the amount of money she spent?

Answer:  $ 4050

Fraction into Percentage

Percentage into Fraction

Percentage into Ratio

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problem solving involving percentages

Home / TEAS Test Review Guide / Solve Problems Involving Percentages: TEAS

Solve Problems Involving Percentages: TEAS

Basic terms and terminology relating to solving problems involving percentages, converting among fractions, decimals, ratios and percentages, calculating problems involving percentages.

problem solving involving percentages

  • Percentages are a number with a % sign that represent numbers in comparison to 100.

Percentages and Their Meaning

Pie Chart

Percentages are a number with a % sign that represent numbers in comparison to 100. As shown in the picture below, of all of the persons using a web browser to access Wikipedia, 20.03 %, or 20.03 people out of every hundred people, used Chrome and 19.26% of all of the persons using a web browser to access Wikipedia, 19.26%, or 19.26 people out of every hundred people, used Firefox, etc.

100% is the whole and it is equal to 1. Percentages less than 100% are less than 1 or the whole and percentages more than 100% are more than one or the whole; and percentages less than 1% are also possible.

Some examples of percentages less than 100% that are less than 1 and less than the whole are:

Some examples of percentages more than 100% that are more than 1 and more than the whole are:

Some examples of percentages less than 1% that are less than the whole AND less than 1 out of every hundred are:

Percentages have equivalents in terms of a fraction, a decimal point number and as a ratio.

You may have noticed a pattern in the chart above suggesting how to convert among fractions, decimals and percentages.

The conversion of percentages into fractions is done by simply placing the percentage number over 100. Regardless of whether or not the percentage number is less than or greater than 100, the denominator of the fraction is always 100

Here are some examples:

  • 12% = 12/100
  • 120% = 120/100
  • 220% = 220/100
  • 2222% = 2222/100

The conversion of percentages into decimal numbers is done by moving the percentage number's decimal place 2 places to the left. As previously discussed, dividing by 100 can be done simply by moving the decimal place two places to the left.

  • 120% = 1.20
  • 220% = 2.20

The conversion of percentages into ratios is done by placing the percentage number and then : (colon) and then 100. A ratio is read as 12 is to 100 when you see 12 : 100. There are 12 per hundred.

  • 12% = 12 : 100
  • 120% = 120 : 100
  • 220% = 220 : 100
  • 2222% = 2222 : 100

In your everyday life, you use and calculate with percentages more than you think.

Here are some of the everyday percentages that you use on a daily or regular basis:

  • BOGO or Buy 1 and Get 1 Free
  • 30% off men's shirts
  • Your weight goal is to lose 5% of your weight every 6 months
  • You financial goal is to save 3% of your annual salary each year

Example 1: Calculating Problems Involving Percentages

Your local grocery store is having a huge BOGO sale this week. You will be purchasing 1 of each of these BOGO items this week and your store does NOT require that you take 2 to get the BOGO discount:

Cereal (usual price is $5.39 per box)

50% of $5.39

1/2 x $5.39 OR 0.5 x $5.39 OR 50% : !00% = x : $5.39

1/2 x $5.39 = $5.29/2 = $2.70 rounded off to the nearest penny

0.5 x $5.39 = $2.70 rounded off to the nearest penny

50% : !00% = x : $5.39

50/100 = x / $5.39

x=$2.70 rounded off to the nearest penny

In this example, you have paid $2.70 per box of cereal and you have also saved $2.69 per box of cereal.

Example 2: Calculating Problems Involving Percentages

You will be purchasing each of these shirts during the 30% off sale. How much will you save with the purchase of these 4 shirts?

  • Blue shirt (Regular price is $19.99)

When shirts are discounted by 30%, you will be paying only 70% of the regular price for the shirt. So, in order to find out what you are saving per shirt, you would have to calculate 30% of the regular price; and, in order to determine what you will be spending for each discounted shirt, you would have to calculate 70% of the regular price.

1/3 x $19.99 OR 0.33 x $19.99 OR 30% : 100% = x : $19.99

1/3 x $19.99 = $19.99/3 = $6.66 rounded off to the nearest penny

0.33 x $19.99 = $6.66 rounder off the nearest penny

30% : 100% = x : $19.99

30/100 = x / $19.99

x = $6.66 rounded off to the nearest penny

In this example, you have saved $6.66 for this blue shirt.

Example 3: Calculating Problems Involving Percentages

When your weight goal is to lose 5% of your weight every 6 months, how much weight should you lose every 6 months when your weight is as follows:

  • Your weight: 160 pounds

5/100 x 160 pounds OR 0.05 x 160 pounds OR 5% : 100% = x : 160 pounds

5 /100 OR 1/20 x 160 pounds = 8 pounds

0.05 x 160 pounds = 8 pounds

5% : 100% = x : 160 pounds

5/100 = x/160

x = 8 pounds

In this example, you should lose 8 pounds every 6 months.

Example 4: Calculating Problems Involving Percentages

  • Your weight: 65 kilograms

5/100 x 65 kg OR 0.05 x 65 kg OR 5% : 100% = x : 65 kg

5/100 OR 1/20 x 65 kg = 3.25 kg

0.05 x 65 kg = 3.25 kg

5% : 100% = x : 65 kg

5/100 = x/65

x = 3.25 kg

In this example, you should lose 3.25 kg every 6 months.

Example 5: Calculating Problems Involving Percentages

  • Your weight: 89 kilograms

5/100 x 89 kg OR 0.05 x 89 kg OR 5% : 100% = x : 89 kg

5/100 OR 1/20 x 89 kg = 4.45 kg

0.05 x 89 kg = 4.45 kg

5% : 100% = x : 89 kg

5/100 = x/89

x = 4.45 kg

In this example, you should lose 4.45 kg every 6 months.

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Alene Burke, RN, MSN

Grade 6 Mathematics Module: Solving Problems Involving Percent

This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.

Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.

Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.

If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.

This module was designed and written with you in mind. It is here to help you master the lessons on solving percent problems such as percent of increase or decrease (discounts, original price, rate of discount, sale price, marked-up price), commission, sales tax, and simple interest. The scope of this module permits it to be used in many different learning situations. The language used recognizes your diverse vocabulary level as student. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.

The module is divided into three lessons, namely:

  • Lesson 1 – Solving Percent Problems Involving Percent of Increase or Decrease
  • Lesson 2 – Solving Percent Problems Involving Markups and Discounts
  • Lesson 3 – Solving Percent Problems Involving Commission, Sales Tax, and Simple Interest

After going through this module, you are expected to solve problems involving percent which can be used in real-life situations, specifically to:

1. identify and analyze the elements of problems or situations involving percent and understand the process in solving each component;

2. visualize problems about percent using illustration to show better understanding in the given situation; and,

3. solve different problems involving percent such as change of percent, markup, discount, commission, sales tax, and simple interest.

Grade 6 Mathematics Quarter 2 Self-Learning Module: Solving Problems Involving Percent

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  1. 5.2.1: Solving Percent Problems

    To solve percent problems, you can use the equation, Percent ⋅ Base = Amount , and solve for the unknown numbers. Or, you can set up the proportion, Percent = amount base , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion. Percents are a ratio of a number and 100, so they are ...

  2. Percentages

    p = a b × 100. This equation can be rearranged to show a or b in terms of the other values: a = p 100 × b b = a ( p 100) = 100 × a p. [Examples] In word problems involving percentages, remember that the sum of all parts of the whole is 100 % . For example, if a teacher has graded 60 % of an assignment, then they have not graded 100 − 60 % ...

  3. Percent Maths Problems

    Solution to Problem 1 The absolute decrease is 20 - 15 = $5 The percent decrease is the absolute decrease divided by the the original price (part/whole). percent decease = 5 / 20 = 0.25 Multiply and divide 0.25 to obtain percent. percent decease = 0.25 = 0.25 * 100 / 100 = 25 / 100 = 25% Problem 2 Mary has a monthly salary of $1200.

  4. Solving percent problems (video)

    25% is part of a whole 100%.*. *25% is 1/4 of 100%*. so, you know that (150) is 1/4 of the answer (100%) Add 150 - 4 times (Because we know that 25% X 4 = 100%) And that is equal to: (150 + 150 + 150 + 150) = *600. The method they used in the video is also correct, but i think that this one is easier, and will make it more simple to solve the ...

  5. Percentages Practice Questions

    The Corbettmaths Practice Questions on finding a percentage of an amount.

  6. How to Solve Percent Problems? (+FREE Worksheet!)

    Solution: Use the following formula: Base \ (= \color { black } {Part} \ ÷ \ \color {blue} {Percent}\) \ (→\) Base \ (=40 \ ÷ \ 0.10=400\) \ (40\) is \ (10\%\) of \ (400\). Percent Problems - Example 3: \ (1.2\) is what percent of \ (24\)? Solution: In this problem, we are looking for the percent. Use the following equation:

  7. Solving problems with percentages

    To solve problems with percent we use the percent proportion shown in "Proportions and percent". a b = x 100 a b = x 100 a b ⋅b = x 100 ⋅ b a b ⋅ b = x 100 ⋅ b a = x 100 ⋅ b a = x 100 ⋅ b x/100 is called the rate. a = r ⋅ b ⇒ Percent = Rate ⋅ Base a = r ⋅ b ⇒ P e r c e n t = R a t e ⋅ B a s e

  8. Solving percent problems

    Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fr...

  9. Different Types of Percentage Problems

    Solution: Total number of fruits shopkeeper bought = 600 + 400 = 1000 Number of rotten oranges = 15% of 600 = 15/100 × 600 = 9000/100 = 90 Number of rotten bananas = 8% of 400 = 8/100 × 400 = 3200/100 = 32 Therefore, total number of rotten fruits = 90 + 32 = 122 Therefore Number of fruits in good condition = 1000 - 122 = 878

  10. Solving Percent Problems

    Problems involving percents have any three quantities to work with: the percent, the amount, and the base. The percent has the percent symbol (%) or the word "percent." In the problem above, 15% is the percent off the purchase price. The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.

  11. PDF Percent Equation P B A

    Percent Proportion. Problems involving the percent equation can also be solved with the proportion: Percent Amount (is) =. 100 Base (of) When the percent is given, drop the percent sign and place the percent over 100. Cross multiply to solve the proportion. Example 2: 27 is 45% of what number?

  12. Fractions, decimals, & percentages

    We'll also solve interesting word problems involving percentages (discounts, taxes, and tip calculations). Converting fractions to decimals Learn Rewriting decimals as fractions: 2.75 Worked example: Converting a fraction (7/8) to a decimal Fraction to decimal: 11/25 Fraction to decimal with rounding Practice

  13. Solve problems involving the calculation of percentages of amounts

    Solve problems involving the calculation of percentages of amounts. In this lesson, we will be learning to find a percentage of an amount, including using efficient strategies and looking at the link between percentages and fractions. ... Solve problems involving the calculation of percentages of amounts. Start. Q1. What is 25% of 400? 4 40 100 ...

  14. Percentages Worksheets

    Welcome to the percentages math worksheet page where we are 100% committed to providing excellent math worksheets. ... Most calculations involving percentages involve using the percentage in its decimal form. This is achieved by dividing the percentage amount by 100. ... Mixed Percent Problems with Whole Number Amounts and Multiples of 5 ...

  15. Solving Problems with Percentages

    Lesson 1. Converting between fractions decimals and percentages Lesson 2. Writing Percentages Lesson 3. Percentage Increases Lesson 4. Percentage Decreases Lesson 5. Reverse Percentages Lesson 6. Compound Percentage Increases Lesson 7. Compound Percentage Decrease Lesson 8. Calculating a Repeated Percentage Change Extended Learning Online Lesson

  16. Calculate percentages with Step-by-Step Math Problem Solver

    Welcome to Quickmath Solvers! Enter the value (s) for the required question and click the adjacent Go button. What is % of ? is what percent of ? is % of what number? What is the fraction / as a percentage? What is the decimal or integer as a percentage? What is % as a fraction? What is % as a decimal? What is the percentage change when becomes ?

  17. Fractions, Decimals and Percentages

    Bouncing Ball Age 11 to 14 Short Challenge Level A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell. Percentage Mad Age 11 to 14 Short Challenge Level Weekly Problem 43 - 2013 What is 20% of 30% of 40% of £50? Information Display Age 11 to 14 Short Challenge Level

  18. Percentage Word Problems with Solutions

    Solution: Given, Total number of marks = 278 Preethi secured marks = 81% Percentage formula = P% × X = Y Where P = 81% Y = 278 Then 81% × X = 278 81/100 × X = 278 X = 278 × 100/81 X = 27800/81 = 343.2 Thus Preethi got 278 marks out of 343.2 marks. Example 2.

  19. Word Problems on Percentage

    Word problems on percentage will help us to solve various types of problems related to percentage. Follow the procedure to solve similar type of percent problems. Word problems on percentage: 1. In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks. Solution: Let the maximum marks be m. Ashley's marks = 83% of m

  20. Solving Problems Involving Percentages

    Solve Problems Involving Percentages: TEAS Basic Terms and Terminology Relating to Solving Problems Involving Percentages Converting Among Fractions, Decimals, Ratios and Percentages Calculating Problems Involving Percentages RegisteredNursing.org Staff Writers | Updated/Verified: Sep 27, 2023

  21. Grade 6 Mathematics Module: Solving Problems Involving Percent

    The module is divided into three lessons, namely: Lesson 1 - Solving Percent Problems Involving Percent of Increase or Decrease. Lesson 2 - Solving Percent Problems Involving Markups and Discounts. Lesson 3 - Solving Percent Problems Involving Commission, Sales Tax, and Simple Interest. After going through this module, you are expected to ...