solve percent problems part 1 iready quiz

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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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Level G is a level that appears in some i-Ready Reading and Math lessons. Level G is equivalent to 7th Grade in the U.S. In these i-Ready lessons , many characters appear. Older lessons were being replaced by new lessons without characters as of 2020, 2021, and 2022. The i-Ready Wiki gives this level a high-level classification.

• 2.2 Deleted Math (pre-August 2019)
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• This level contains one of the only three-part sub-series, "Solve Percent Problems.” The other one is "Multiplicative Comparison Word Problems, Part 3" in Level D .
• Many of the newer lessons with characters don't appear in this level, making a huge crash for the i-Ready newer lesson rate.
• Understanding Informational Texts About Preparing for Space ( Reading ) has a typo in the second Instruction question.
• Since 2019, Curriculum Associates has been phasing out older lessons and making newer ones to replace them. The new lessons are less time consuming and have no characters in them. The main reason they did this is some students did not like the characters talking. They wanted to learn without the characters. They have been moved to extra. They have also been doing this for Levels C - H .
• Level G could be considered the first level in the middle school line for some grade systems.

Lessons [ ]

• Understand Addition with Integers (Mid 7) (Number and Operations)
• Understand Subtraction with Integers (Math) (Mid 7) (Number and Operations)
• Practice: Add and Subtract Integers (Math) (Mid 7) (Number and Operations)
• Strategies to Add and Subtract Integers (Math) (Mid 7) (Number and Operations)
• Practice: Strategies to Add and Subtract Integers (Math) (Mid 7) (Number and Operations)
• Understand Distance on the Number Line (Mid 7) (Number and Operations)
• Practice: Add and Subtract Rationals (Mid 7) (Number and Operations)
• Strategies to Add and Subtract Rationals (Mid 7) (Number and Operations)
• Practice: Strategies to Add and Subtract Rationals (Math) (Number and Operations)
• Understand Distance on the Number Line (Mid 7) (Numbers and Operations)
• Add and Subtract Rationals (Mid 7) (Math) (Numbers and Operations)
• Practice: Add and Subtract Rationals (Mid 7) (Math) (Numbers and Operations)
• Multiply Integers (Math) (Number and Operations)
• Divide Integers (Math) (Number and Operations)
• Practice: Multiply and Divide Integers (Math) (Number and Operations)
• Multiply and Divide Rationals (Math) (Number and Operations)
• Practice: Multiply and Divide Rationals (Math) (Number and Operations)
• Express Rational Numbers as Decimals (Math) (Number and Operations)
• Solve Problems with Rational Numbers (Math) (Number and Operations)
• Unit Rates involving Ratios with Fractions, Part 1 (Math) (Algebra and Algebraic Thinking)
• Unit Rates involving Ratios with Fractions, Part 2 (Math) (Algebra and Algebraic Thinking)
• Practice: Unit Rates involving Ratios with Fractions (Math) (Algebra and Algebraic Thinking)
• Understand Proportional Relationships (Math) (Algebra and Algebraic Thinking)
• Write Equations for Proportional Relationships (Math) (Algebra and Algebraic Thinking)
• Practice: Proportional Relationships (Math) (Algebra and Algebraic Thinking)
• Equivalent Linear Expressions (Math) (Algebra and Algebraic Thinking)
• Practice: Equivalent Linear Expressions (Math) (Algebra and Algebraic Thinking)
• Reasons for Equivalent Linear Expressions (Math) (Algebra and Algebraic Thinking)
• Understand Multi-Step Equations (Math) (Algebra and Algebraic Thinking)
• Solve Multi-Step Equations, Part 1 (Math) (Algebra and Algebraic Thinking)
• Solve Multi-Step Equations, Part 2 (Math) (Algebra and Algebraic Thinking)
• Write and Solve Multi-Step Equations (Math) (Algebra and Algebraic Thinking)
• Practice: Write and Solve Multi-Step Equations (Math) (Algebra and Algebraic Thinking)
• Understand Solutions of Inequalities (Math) (Algebra and Algebraic Thinking)
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• Solve Problems with Inequalities (Math) (Algebra and Algebraic Thinking)
• Solve Percent Problems, Part 1 (Math) (Algebra and Algebraic Thinking)
• Practice: Solve Percent Problems (Math) (Algebra and Algebraic Thinking)
• Solve Percent Problems, Part 2 (Math) (Algebra and Algebraic Thinking)
• Solve Percent Problems, Part 3 (Math) (Algebra and Algebraic Thinking)
• Percent Change (Math) (Algebra and Algebraic Thinking)
• Understand Random Sampling (Math) (Measurement and Data)
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• Compare Populations (Math) (Measurement and Data)
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• Understand Scale Drawings (Math) (Geometry)
• Use Scale Factors (Math) (Geometry)
• Understand Area and Circumference of a Circle (Math) (Geometry)
• Understand Angle Relationships (Math) (Geometry)
• Area and Surface Area (Math) (Geometry)
• Volume of Composed Figures (Math) (Geometry)

Deleted Math (pre-August 2019) [ ]

• Adding and Subtracting Integers (Number and Operations)
• Adding and Subtracting Rational Numbers (Number and Operations)
• Multiplication and Division of Integers (Number and Operations)
• Recognizing Proportional Relationships (Algebra and Algebraic Thinking)
• Equations for Proportional Relationships (Algebra and Algebraic Thinking)
• Problem Solving with Proportional Relationships (Algebra and Algebraic Thinking)

Deleted Math (pre-August 2020) [ ]

• Multiplication and Division of Rational Numbers (Number and Operations)
• Problem Solving with Rational Numbers (Algebra and Algebraic Thinking)
• Ratios Involving Complex Fractions (Algebra and Algebraic Thinking)
• Linear Expressions (Algebra and Algebraic Thinking)
• Problem Solving with Equations (Algebra and Algebraic Thinking)
• Problem Solving with Inequalities (Algebra and Algebraic Thinking)

Extra Math [ ]

• Random Samples (Math) (Extra)
• Making Statistical Inferences (Math) (Extra)
• Using Mean and Mean Absolute Deviation to Compare Data (Math) (Extra)
• Using Measures of Center and Variability to Compare Data (Math) (Extra)
• Probability Concepts (Math) (Extra)
• Experimental Probability (Math) (Extra)
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• Simulations of Compound Events (Math) (Extra)
• Construction of Triangles (Math) (Extra)
• Area and Circumference of a Circle (Math) (Extra)

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• Identifying Replaced Words and Ideas in Literary Texts (Reading) (Early 7)
• Citing Evidence: Literary Text (Reading)
• Identifying Replaced Words and Ideas in Informational Texts (Reading)
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• Vocabulary about Protecting Nature: Preview 1 (Reading)
• Analyzing Sentence Parts in Literary Text (Reading)
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• Vocabulary about Improving the World: Preview 1 (Reading)
• Analyzing Sentence Parts in Informational Texts (Reading)
• Vocabulary about Improving the World: Preview 2 (Reading)
• Summarizing Social Studies Texts (Reading)
• Vocabulary about Improving the World: Assess (Reading)
• Understanding Literary Texts About Creative Solutions (Reading)
• Analyzing How Story Elements Interact (Reading)
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• Vocabulary about Seaside Life: Preview 1 (Reading)
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• Determining Word Meaning: Literary Text (Reading)
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• Comparing Texts on the Same Topic (Reading)
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Extra Reading [ ]

• Determining Word Meaning using Context Clues (Carrie, Brandi, Max) (Reading) (Extra)
• Understanding Connotative Meanings (Jake, Sweet T, Pepper Jackie) (Reading) (Extra)
• Using Greek and Latin Roots and Affixes (Alex, Ray, Dayrl, Edbird) (Reading) (Extra)
• Understanding the Relationship between Words (Carrie, Brandi, Max) (Reading) (Extra)
• 3 I-Ready Lessons

i-Ready Solve Percent Problems, Part 1 — Instruction — Level G × ◀ Clementine earns a total of $150 per week. She must pay 11% of her total earnings in taxes. Clementine wants to know how much of her earnings are left over after taxes are paid. How much does Clementine pay in taxes?

Gauth ai solution.