how to solve ratios in word problems

• Parallelogram
• Quadrilateral
• Parallelepiped
• Tetrahedron
• Dodecahedron
• Fraction Calculator
• Mixed Fraction Calculator
• Greatest Common Factor Calulator
• Decimal to Fraction Calculator
• Whole Numbers
• Rational Numbers
• Place Value
• Irrational Numbers
• Natural Numbers
• Binary Operation
• Numerator and Denominator
• Order of Operations (PEMDAS)
• Scientific Notation

Last modified on August 3rd, 2023

Ratio Word Problems

Here, we will learn to do some practical word problems involving ratios.

Amelia and Mary share $40 in a ratio of 2:3. How much do they get separately?

There is a total reward of $40 given.  Let Amelia get = 2x and Mary get = 3x Then, 2x + 3x = 40 Now, we solve for x => 5x = 40 => x = 8 Thus, Amelia gets = 2x = 2 × 8 = $16 Mary gets = 3x = 3 × 8 = $24

In a bag of blue and red marbles, the ratio of blue marbles to red marbles is 3:4. If the bag contains 120 green marbles, how many blue marbles are there?

Let the total number of blue marbles be x Thus, ${\dfrac{3}{4}=\dfrac{x}{120}}$ x = ${\dfrac{3\times 120}{4}}$ x = 90 So, there are 90 blue marbles in the bag.

Gregory weighs 75.7 kg. If he decreases his weight in the ratio of 5:4, find his reduced weight.

Let the decreased weight of Gregory be = x kg Thus, 5x = 75.7 x = \dfrac{75\cdot 7}{5} = 15.14 Thus his reduced weight is 4 × 15.14 = 60.56 kg

A recipe requires butter and sugar to be in the ratio of 2:3. If we require 8 cups of butter, find how many cups of sugar are required. Write the equivalent fraction.

Thus, for every 2 cups of butter, we use 3 cups of sugar Here we are using 8 cups of butter, or 4 times as much So you need to multiply the amount of sugar by 4 3 × 4 = 12 So, we need to use 12 cups of sugar Thus, the equivalent fraction is ${\dfrac{2}{3}=\dfrac{8}{12}}$

Jerry has 16 students in his class, of which 10 are girls. Write the ratio of girls to boys in his class. Reduce your answer to its simplest form.

Total number of students = 16 Number of girls = 10 Number of boys = 16 – 10 = 6 Thus the ratio of girls to boys is ${\dfrac{10}{6}=\dfrac{5}{3}}$

A bag containing chocolates is divided into a ratio of 5:7. If the larger part contains 84 chocolates, find the total number of chocolates in the bag.

Let the total number of chocolates be x

Then the two parts are:

${\dfrac{5x}{5+7}}$ and ${\dfrac{7x}{5+7}}$

${\dfrac{7x}{5+7}}$ = 84

=> ${\dfrac{7x}{12}}$ = 84

Thus, the total number of chocolates that were present in the bag was 144

Leave a comment Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

• Privacy Policy
• Trigonometry

Join Our Newsletter

© 2024 Mathmonks.com . All rights reserved. Reproduction in whole or in part without permission is prohibited.

One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

In order to access this I need to be confident with:

This topic is relevant for:

Ratio Problem Solving

Here we will learn about ratio problem solving, including how to set up and solve problems. We will also look at real life ratio problems.

There are also ratio problem solving worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is ratio problem solving?

Ratio problem solving is a collection of word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.

A ratio is a relationship between two or more quantities . They are usually written in the form a:b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are,

• What is the ratio involved?
• What order are the quantities in the ratio?
• What is the total amount / what is the part of the total amount known?
• What are you trying to calculate ?

As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that we can use to help us find an answer. 

The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution.

Let’s look at a couple of methods we can use when given certain pieces of information.

When solving ratio problems it is very important that you are able to use ratios. This includes being able to use ratio notation. 

For example, Charlie and David share some sweets in the ratio of 3:5. This means that for every 3 sweets Charlie gets, David receives 5 sweets.

Charlie and David share 40 sweets, how many sweets do they each get?

We use the ratio to divide 40 sweets into 8 equal parts. 

Then we multiply each part of the ratio by 5.

3 x 5:5 x 5 = 15:25

This means that Charlie will get 15 sweets and David will get 25 sweets.

• Dividing ratios

Step-by-step guide: Dividing ratios (coming soon)

Ratios and fractions (proportion problems)

We also need to consider problems involving fractions. These are usually proportion questions where we are stating the proportion of the total amount as a fraction.

Simplifying and equivalent ratios

• Simplifying ratios

Equivalent ratios

Units and conversions ratio questions

Units and conversions are usually equivalent ratio problems (see above).

• If £1:\$1.37 and we wanted to convert £10 into dollars, we would multiply both sides of the ratio by 10 to get £10 is equivalent to \$13.70.
• The scale on a map is 1:25,000. I measure 12cm on the map. How far is this in real life, in kilometres? After multiplying both parts of the ratio by 12 you must then convert 12 \times 25000=300000 \ cm to km by dividing the solution by 100 \ 000 to get 3km.

Notice that for all three of these examples, the units are important. For example if we write the mapping example as the ratio 4cm:1km, this means that 4cm on the map is 1km in real life.

Top tip: if you are converting units, always write the units in your ratio.

Usually with ratio problem solving questions, the problems are quite wordy . They can involve missing values , calculating ratios , graphs , equivalent fractions , negative numbers , decimals and percentages .

Highlight the important pieces of information from the question, know what you are trying to find or calculate , and use the steps above to help you start practising how to solve problems involving ratios.

How to do ratio problem solving

In order to solve problems including ratios:

Identify key information within the question.

Know what you are trying to calculate.

Use prior knowledge to structure a solution.

Explain how to do ratio problem solving

Ratio problem solving worksheet

Get your free ratio problem solving worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on ratio

Ratio problem solving is part of our series of lessons to support revision on ratio . You may find it helpful to start with the main ratio lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• How to work out ratio  
• Ratio to fraction
• Ratio scale
• Ratio to percentage

Ratio problem solving examples

Example 1: part:part ratio.

Within a school, the number of students who have school dinners to packed lunches is 5:7. If 465 students have a school dinner, how many students have a packed lunch?

Within a school, the number of students who have school dinners to packed lunches is \bf{5:7.} If \bf{465} students have a school dinner , how many students have a packed lunch ?

Here we can see that the ratio is 5:7 where the first part of the ratio represents school dinners (S) and the second part of the ratio represents packed lunches (P).

We could write this as

Where the letter above each part of the ratio links to the question.

We know that 465 students have school dinner.

2 Know what you are trying to calculate.

From the question, we need to calculate the number of students that have a packed lunch, so we can now write a ratio below the ratio 5:7 that shows that we have 465 students who have school dinners, and p students who have a packed lunch.

We need to find the value of p.

3 Use prior knowledge to structure a solution.

We are looking for an equivalent ratio to 5:7. So we need to calculate the multiplier. We do this by dividing the known values on the same side of the ratio by each other.

So the value of p is equal to 7 \times 93=651.

There are 651 students that have a packed lunch.

Example 2: unit conversions

The table below shows the currency conversions on one day.

Use the table above to convert £520 (GBP) to Euros € (EUR).

Use the table above to convert \bf{£520} (GBP) to Euros \bf{€} (EUR).

The two values in the table that are important are GBP and EUR. Writing this as a ratio, we can state

We know that we have £520.

We need to convert GBP to EUR and so we are looking for an equivalent ratio with GBP = £520 and EUR = E.

To get from 1 to 520, we multiply by 520 and so to calculate the number of Euros for £520, we need to multiply 1.17 by 520.

1.17 \times 520=608.4

So £520 = €608.40.

Example 3: writing a ratio 1:n

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the 500ml of concentrated plant food must be diluted into 2l of water. Express the ratio of plant food to water respectively in the ratio 1:n.

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the \bf{500ml} of concentrated plant food must be diluted into \bf{2l} of water . Express the ratio of plant food to water respectively as a ratio in the form 1:n.

Using the information in the question, we can now state the ratio of plant food to water as 500ml:2l. As we can convert litres into millilitres, we could convert 2l into millilitres by multiplying it by 1000.

2l = 2000ml

So we can also express the ratio as 500:2000 which will help us in later steps.

We want to simplify the ratio 500:2000 into the form 1:n.

We need to find an equivalent ratio where the first part of the ratio is equal to 1. We can only do this by dividing both parts of the ratio by 500 (as 500 \div 500=1 ).

So the ratio of plant food to water in the form 1:n is 1:4.

Example 4: forming and solving an equation

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives £8 pocket money, how much money do the three siblings receive in total?

Three siblings, Josh, Kieran and Luke, receive pocket money per week proportional to their ages. Kieran is \bf{3} years older than Josh . Luke is twice Josh’s age. If Luke receives \bf{£8} pocket money, how much money do the three siblings receive in total ?

We can represent the ages of the three siblings as a ratio. Taking Josh as x years old, Kieran would therefore be x+3 years old, and Luke would be 2x years old. As a ratio, we have

We also know that Luke receives £8.

We want to calculate the total amount of pocket money for the three siblings.

We need to find the value of x first. As Luke receives £8, we can state the equation 2x=8 and so x=4.

Now we know the value of x, we can substitute this value into the other parts of the ratio to obtain how much money the siblings each receive.

The total amount of pocket money is therefore 4+7+8=£19.

Example 5: simplifying ratios

Below is a bar chart showing the results for the colours of counters in a bag.

Express this data as a ratio in its simplest form.

From the bar chart, we can read the frequencies to create the ratio.

We need to simplify this ratio.

To simplify a ratio, we need to find the highest common factor of all the parts of the ratio. By listing the factors of each number, you can quickly see that the highest common factor is 2.

\begin{aligned} &12 = 1, {\color{red} 2}, 3, 4, 6, 12 \\\\ &16 = 1, {\color{red} 2}, 4, 8, 16 \\\\ &10 = 1, {\color{red} 2}, 5, 10 \end{aligned}

HCF (12,16,10) = 2

Dividing all the parts of the ratio by 2 , we get

Our solution is 6:8:5 .

Example 6: combining two ratios

Glass is made from silica, lime and soda. The ratio of silica to lime is 15:2. The ratio of silica to soda is 5:1. State the ratio of silica:lime:soda.

Glass is made from silica, lime and soda. The ratio of silica to lime is \bf{15:2.} The ratio of silica to soda is \bf{5:1.} State the ratio of silica:lime:soda .

We know the two ratios

We are trying to find the ratio of all 3 components: silica, lime and soda.

Using equivalent ratios we can say that the ratio of silica:soda is equivalent to 15:3 by multiplying the ratio by 3.

We now have the same amount of silica in both ratios and so we can now combine them to get the ratio 15:2:3.

Example 7: using bar modelling

India and Beau share some popcorn in the ratio of 5:2. If India has 75g more popcorn than Beau, what was the original quantity?

India and Beau share some popcorn in the ratio of \bf{5:2.} If India has \bf{75g} more popcorn than Beau , what was the original quantity?

We know that the initial ratio is 5:2 and that India has three more parts than Beau.

We want to find the original quantity.

Drawing a bar model of this problem, we have

Where India has 5 equal shares, and Beau has 2 equal shares.

Each share is the same value and so if we can find out this value, we can then find the total quantity.

From the question, India’s share is 75g more than Beau’s share so we can write this on the bar model.

We can find the value of one share by working out 75 \div 3=25g.

We can fill in each share to be 25g.

Adding up each share, we get

India = 5 \times 25=125g

Beau = 2 \times 25=50g

The total amount of popcorn was 125+50=175g.

Common misconceptions

• Mixing units

Make sure that all the units in the ratio are the same. For example, in example 6 , all the units in the ratio were in millilitres. We did not mix ml and l in the ratio.

• Ratio written in the wrong order

For example the number of dogs to cats is given as the ratio 12:13 but the solution is written as 13:12.

• Ratios and fractions confusion

Take care when writing ratios as fractions and vice-versa. Most ratios we come across are part:part. The ratio here of red:yellow is 1:2. So the fraction which is red is \frac{1}{3} (not \frac{1}{2} ).

• Counting the number of parts in the ratio, not the total number of shares

For example, the ratio 5:4 has 9 shares, and 2 parts. This is because the ratio contains 2 numbers but the sum of these parts (the number of shares) is 5+4=9. You need to find the value per share, so you need to use the 9 shares in your next line of working.

• Ratios of the form \bf{1:n}

The assumption can be incorrectly made that n must be greater than 1 , but n can be any number, including a decimal.

Practice ratio problem solving questions

1. An online shop sells board games and computer games. The ratio of board games to the total number of games sold in one month is 3:8. What is the ratio of board games to computer games?

8-3=5 computer games sold for every 3 board games.

2. The volume of gas is directly proportional to the temperature (in degrees Kelvin). A balloon contains 2.75l of gas and has a temperature of 18^{\circ}K. What is the volume of gas if the temperature increases to 45^{\circ}K?

3. The ratio of prime numbers to non-prime numbers from 1-200 is 45:155. Express this as a ratio in the form 1:n.

4. The angles in a triangle are written as the ratio x:2x:3x. Calculate the size of each angle.

5. A clothing company has a sale on tops, dresses and shoes. \frac{1}{3} of sales were for tops, \frac{1}{5} of sales were for dresses, and the rest were for shoes. Write a ratio of tops to dresses to shoes sold in its simplest form.

6. During one month, the weather was recorded into 3 categories: sunshine, cloud and rain. The ratio of sunshine to cloud was 2:3 and the ratio of cloud to rain was 9:11. State the ratio that compares sunshine:cloud:rain for the month.

Ratio problem solving GCSE questions

1. One mole of water weighs 18 grams and contains 6.02 \times 10^{23} water molecules.

Write this in the form 1gram:n where n represents the number of water molecules in standard form.

2. A plank of wood is sawn into three pieces in the ratio 3:2:5. The first piece is 36cm shorter than the third piece.

Calculate the length of the plank of wood.

5-3=2 \ parts = 36cm so 1 \ part = 18cm

3. (a) Jenny is x years old. Sally is 4 years older than Jenny. Kim is twice Jenny’s age. Write their ages in a ratio J:S:K.

(b) Sally is 16 years younger than Kim. Calculate the sum of their ages.

Learning checklist

You have now learned how to:

• Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
• Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
• Make and use connections between different parts of mathematics to solve problems

The next lessons are

• Compound measures
• Best buy maths

Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.

Privacy Overview

Become a math whiz with AI Tutoring, Practice Questions & more.

Word Problems: Ratios

When we solve word problems, we often encounter ratios. Whether we're aware of it or not, our universe contains many ratios -- including the so-called " golden ratio " that is so common in nature. When we understand how ratios work, it's easy to solve all kinds of real-world problems . Let's get started:

What is a ratio?

A ratio is a comparison of two different values with the same units. We write these with colons. Here are a few examples: 5:1, 12:30, 1:2

The colon simply means "to," so "5:1" means a "five to one" ratio.

Using our knowledge of ratios to solve word problems

Let's use our knowledge of ratios to tackle a few word problems:

Let's say we have 12 sunfish and 30 rainbow shiners in our backyard pond. What is the ratio of sunfish to rainbow shiners in its simplest form?

We can write the ratio 12:30 as the fraction 12 30 . Next, we can reduce this fraction to 2/5. Finally, we rewrite it as the ratio 2:5. We also know that the reverse is true, as the ratio of rainbow shiners to sunfish is 5:2.

Now let's say we have a classroom of 32 students with 20 girls. What is the ratio of boys to girls?

We know that the total is 32 -- but we can't make the mistake of giving 20/32 as our answer. This gives us the ratio of girls to the total number of students -- but it doesn't give us the ratio of girls to boys. To find the correct answer, we need the total number of boys.

30 - 18 = 12 boys

Therefore, the ratio of girls to boys is 20:12 or 5:3 in simplified terms.

Now let's say we're baking a cake using a recipe that calls for a butter-to-sugar ratio of 2:3. If we use 6 cups of butter, how many cups of sugar should we use?

We know that we're using three times as much butter as the original recipe (since 6 is three times 2), so all we need to do is multiply the original sugar amount by three as well.

3 × 3 = 9 cups of sugar.

So, if we use 6 cups of butter, we should use 9 cups of sugar to maintain the 2:3 butter-to-sugar ratio.

Topics related to the Word Problems: Ratios

Equivalent Ratios

Word Problems

Golden Ratio

Flashcards covering the Word Problems: Ratios

Algebra 1 Flashcards

College Algebra Flashcards

Practice tests covering the Word Problems: Ratios

Algebra 1 Diagnostic Tests

College Algebra Diagnostic Tests

Help your student reach for their math goals

Tutoring helps students reach for their top math goals, whether that involves new challenges outside of the normal curriculum or catching up with their peers. Our Educational Directors will create a tutoring plan for your student that matches up with their goals and their busy schedule, so contact Varsity Tutors today to get started.

• Ohio Bar Exam Test Prep
• NBDE Test Prep
• DAT Test Prep
• 9th Grade Science Tutors
• Professional Certifications Tutors
• USMLE Courses & Classes
• SAT Subject Test in German Courses & Classes
• Red Hat Certified System Administrator Courses & Classes
• Japanese Lessons
• Applied Ethics Tutors
• CPE - Certificate of Proficiency in English Test Prep
• CLEP Introductory Business Law Courses & Classes
• Information Systems Tutors
• Computational Finance Tutors
• Windows Tutors
• ANCC - American Nurses Credentialing Center Test Prep
• SOPD - System Operator / Power Dispatching Test Test Prep
• ASE - National Institute for Automotive Service Excellence Training
• ACCUPLACER Tutors
• SAT Subject Test in French Courses & Classes
• Indianapolis Tutoring
• Miami Tutoring
• Dayton Tutoring
• Virginia Beach Tutoring
• Las Vegas Tutoring
• Salt Lake City Tutoring
• Albany Tutoring
• Richmond Tutoring
• Buffalo Tutoring
• Spokane Tutoring
• Reading Tutors in Washington DC
• Biology Tutors in Philadelphia
• LSAT Tutors in Los Angeles
• SAT Tutors in Houston
• ISEE Tutors in San Francisco-Bay Area
• Algebra Tutors in Seattle
• MCAT Tutors in Miami
• SAT Tutors in New York City
• Reading Tutors in Los Angeles
• ISEE Tutors in Atlanta

Solving Word Problems with Ratios

Hey guys! Welcome to this video tutorial on word problems involving ratios .

Ratios are what we use to compare certain number values. People everywhere use ratios. We use, or at least we should, use ratios when we cook. For example, if I were to make macaroni and cheese for a group of 6 people and I knew that a \(\frac{1}{2}\) cup of macaroni would feed one person, then I could multiply 6 times \(\frac{1}{2}\) to get 3. Well, 3 to 6 is my ratio, and this ratio tells me that for every 3 cups of macaroni that I have, I can serve 6 people.

But hang on. What if I told you that 1 cup of macaroni to every 2 persons is the same ratio as 3:6? Well, it’s the same ratio. 3:6 can be reduced to 1:2 because both 3 and 6 are divisible by 3, which is how we get \(\frac{1}{2}\). So, even though these two ratios look different, they are actually the same.

Let’s take a look at a few word problems, and practice working through them.

Example Problem 1

There are 7 kids in a classroom with green shirts, 8 with red shirts, and 10 with yellow shirts. What is the ratio of people with red and yellow shirts? 7:10 8:7 8:10 4:5

Alright, so let’s look at our problem, and see what it is asking us to find, and write out the information that we have been given.

So, there are 7 kids with green shirts; so, let’s write that down. We have Green: 7. We have 8 kids with red shirts, so that is Red: 8, and we have 10 kids with yellow shirts, Yellow: 10.

So now let’s look at each of our options and eliminate. It can’t be 7:10, we don’t care about the green shirts. It can’t be 8:7, because again we don’t care about the green shirts. Option C is correct; that is the exact number ratio we found. Now, look closely at D here. Is 4:5 not the same thing as 8:10? 8 and 10 are both divisible by 2, and when we reduce them both down we get 4:5, so D is also correct!

Great, now let’s look at another word problem.

Example Problem 2

A vegetable tray contains 12 baby carrots, 27 cherry tomatoes, 18 florets of broccoli, and 45 slices of red bell peppers. For every 2 baby carrots, there are 3_____.

Alright, let’s start off the same way that we did our last problem; read through the problem, write down what we know, and find out what is being asked.

So, this vegetable tray contains 12 baby carrots. It contains 27 cherry tomatoes. We have 18 broccoli florets and 45 slices of red bell peppers.

When we look at all of our information written down, we can see that we have 18 broccoli florets; so there is our answer. For every 2 baby carrots, there are 3 broccoli florets.

Another way to check and verify that these two ratios are equal is by setting them up in fraction form and cross multiplying.

\(\frac{2}{3}=\frac{12}{18}\)

When we cross multiply, we get \(36=36\).

You can practice finding ratios anywhere you go, like finding the ratio of boys to girls in your class.

I hope that this video helped you to understand how to solve word problems with ratios.

See you guys next time!

Frequently Asked Questions

How do you figure out ratios.

A ratio is simply a comparison between two amounts. When figuring out ratios, it is important to consider what two values are being compared. This can be expressed in fraction form, in word form, or simply by using a colon.

When writing a ratio that is comparing a “part” to the “whole”, list the “part” first, and the “whole” second. For example, if you eat \(3\) slices of pizza out of \(10\) slices total, you have eaten \(3\) out of \(10\) slices. This can be expressed as \(\frac{3}{10}\) or \(3\):\(10\), where the part is listed first, and the whole is listed second.

Ratios can also be “part” to “part” comparisons. For example, if there are \(7\) boys in a class, and \(9\) girls in a class, the ratio of boys to girls is \(7\):\(9\). Make sure to match the order of the ratio to the order presented in the scenario.

What are basic ratios?

Ratios are used to directly compare two amounts. Basic ratios are used in many real-world situations, which makes it a valuable skill to master. Basic ratios can be expressed as fractions, words, or by using a colon. For example, \(\frac{4}{5}\), “four to five”, and \(4\):\(5\), all represent the same ratio.

What are the 3 ways to write a ratio?

A ratio is the comparison between two quantities. There is more than one way to write a ratio. For example, ratios can be written using a fraction bar, using a colon, or using words.

\(\frac{5}{8}\) \(5\):\(8\) \(\text{five to eight}\)

What are equivalent ratios?

Ratios that have the same value are considered equivalent ratios . For example, if you slice a cake into \(10\) pieces, and you eat \(2\) pieces, you have eaten “\(2\) out of \(10\)” pieces, or \(2\):\(10\). If you had sliced the cake into \(20\) pieces, and eaten \(4\) pieces, you would have eaten the same amount of cake. Eating “4 out of 20” pieces is the same amount as eating “2 out of 10” pieces. Equivalent ratios occur when you multiply or divide both quantities of the ratio by the same amount. \(\frac{50}{100}\) is equivalent to \(\frac{5}{10}\) because when you divide both quantities of the ratio by \(10\), the result is \(\frac{5}{10}\).

How do you find an equivalent ratio?

Equivalent ratios can be thought of as equivalent fractions. Two ratios are equivalent if they represent the same amount. For example \(\frac{1}{2}\) and \(\frac{5}{10}\) are equivalent because they represent the same amount. Equivalent ratios are found by multiplying or dividing the numerator and denominator by the same amount. For example, \(3\):\(4\) and \(15\):\(20\) are equivalent ratios because both values in \(3\):\(4\) can be multiplied by \(5\) in order to create the ratio \(15\):\(20\).

How do you solve ratio word problems?

Ratios have many real-world applications. Word problems that involve ratios will usually require you to find an unknown value by finding an equivalent ratio.

For example, if you made \($170\) washing \(10\) cars, how much money did you make per car? The ratio of dollars earned compared to cars washed is \(\frac{170}{10}\). We can divide both of these values by \(10\) in order to solve for the dollars earned for washing \(1\) car. \(\frac{170\div10}{10\div10}=\frac{17}{1}\). This means that \($17\) was earned per car. Many word problems involving ratios require you to create equivalent ratios. Remember, as long as you multiply or divide both values of a ratio by the same amount, you have not changed the ratio.

How do you write a ratio in words?

Ratios are used to compare two quantities. There are generally two ways to write a ratio in word form. When a ratio is considered a “part-out-of-whole” ratio, the phrase “out of” can be used. For example, if there is a pizza with \(8\) slices, and you eat \(2\) of those slices, you have eaten “\(2\) out of \(8\)” slices. However, some ratios are considered “part-to-part” ratios. For example, when comparing \(3\) green marbles to \(8\) red marbles, the phrase “\(3\) to \(8\)” can be used.

How do you explain ratios and proportions?

Ratios describe the relationship between two amounts. Ratios can be described as part-to-part or part-to-whole. For example, in a new litter of puppies, \(4\) of the pups are female and \(3\) of the pups are male. The part-to-part ratio \(4\):\(3\) would be used to compare female to male pups. When comparing female pups to the whole liter, the part-to-whole ratio \(4\):\(7\) would be used. Similarly, the ratio of male pups to total pups would be \(3\):\(7\). If two ratios are equivalent, they are said to be proportional. For example, if \(50\) meters of rope weighs \(5\) kilograms, and \(150\) meters of rope weighs \(15\) kilograms, the two amounts are proportional. \(50\):\(5\) is equivalent to \(150\):\(15\) because both values of the first ratio are multiplied by \(3\) in order to create the second ratio.

What is a ratio, short answer?

A ratio is a comparison between two amounts. Ratios can be written using a fraction bar \((\frac{3}{4})\), using a colon (\(3\):\(4\)), or using words (“three to four”). Ratios can be “part-to-part” or “part-to-whole”. For example, \(5\) green marbles and \(7\) red marbles would be a “part-to-part” ratio (\(5\):\(7\)). Solving \(95\) problems correctly out of \(100\) on a math test would be a “part-to-whole” ratio (\(95\):\(100\)).

Ratio Word Problems

  Cross multiply in order to determine which pair of ratios are equivalent.

3:5 and 4:9

6:7 and 7:8

7:8 and 35:40

12:25 and 14:17

The correct answer is 7:8 and 35:40. We can use cross multiplication to determine if two ratios are equivalent. Let’s look at the ratios for Choice C, and let’s set these up as fractions: \(\frac{7}{8}\) and \(\frac{35}{40}\)

Now, cross multiply by finding the product of \(8×35\) and \(7×40\). In both cases our product is 280, so we know that the original ratios are equivalent.

  Which ratio is equivalent to \(\frac{36}{45}\)?

The correct answer is 4:5. We can simplify ratios with the same strategy that we use to simplify fractions. In the ratio \(\frac{36}{45}\) we can divide the numerator and denominator by 9. \(\frac{36}{45}\) now becomes \(\frac{4}{5}\) or 4:5.

  James has a bag full of red, blue, and yellow candy. There are 10 red candies, 9 blue candies, and 11 yellow candies. What is the ratio of blue candies to total candies in the bag? Simplify the ratio if possible.

The correct answer is 3:10. The total number of blue candies is 9, and the total number of candies in the bag is 30. If we set this ratio up as a fraction, we have \(\frac{9}{30}\). This fraction can be simplified if we divide the numerator and denominator by 3. Our final answer is \(\frac{3}{10}\) or 3:10.

  Alex is counting the coins in his pocket, and finds that he has 14 quarters, 7 nickels, and 4 dimes. What is the ratio of quarters to nickels? Simplify if possible.

The correct answer is 2:1. We can compare the number of quarters to the number of nickels by setting up a ratio. There are 14 quarters and 7 nickels, so our ratio would be 14:7. Choice B says 14:7, but we should simplify when possible. 14:7 simplifies to 2:1.

  In Mr. Jenkin’s 4th grade class there are 14 boys and 17 girls. What is the ratio of boys to girls? Simplify if possible.

The correct answer is 14:17. We can express this comparison of boys to girls as a ratio. 14 boys and 17 girls can be described as the ratio 14:17, or the fraction \(\frac{14}{17}\). 14 and 17 do not have any factors in common, so 14:17 is in simplest form.

Return to Basic Arithmetic Videos

by Mometrix Test Preparation | This Page Last Updated: December 28, 2023

Ratio and Percent Word Problems

Ratio word problems, using table with multiplication.

Using Double Number Lines

Using Tape Diagram

Using Graphs

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

• Number Charts
• Multiplication
• Long division
• Basic operations
• Telling time
• Place value
• Roman numerals
• Fractions & related
• Add, subtract, multiply,   and divide fractions
• Mixed numbers vs. fractions
• Equivalent fractions
• Prime factorization & factors
• Fraction Calculator
• Decimals & Percent
• Add, subtract, multiply,   and divide decimals
• Fractions to decimals
• Percents to decimals
• Percentage of a number
• Percent word problems
• Classify triangles
• Classify quadrilaterals
• Circle worksheets
• Area & perimeter of rectangles
• Area of triangles & polygons
• Coordinate grid, including   moves & reflections
• Volume & surface area
• Pre-algebra
• Square Roots
• Order of operations
• Scientific notation
• Proportions
• Ratio word problems
• Write expressions
• Evaluate expressions
• Simplify expressions
• Linear equations
• Linear inequalities
• Graphing & slope
• Equation calculator
• Equation editor
• Elementary Math Games
• Addition and subtraction
• Math facts practice
• The four operations
• Factoring and number theory
• Geometry topics
• Middle/High School
• Statistics & Graphs
• Probability
• Trigonometry
• Logic and proof
• For all levels
• Favorite math puzzles
• Favorite challenging puzzles
• Math in real world
• Problem solving & projects
• For gifted children
• Math history
• Math games and fun websites
• Interactive math tutorials
• Math help & online tutoring
• Assessment, review & test prep
• Online math curricula

Use the generator to make customized ratio worksheets. Experiment with the options to see what their effect is.

Primary Grade Challenge Math by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Unit 3: Ratios and rates

About this unit.

Learn all about proportional relationships. How are they connected to ratios and rates? What do their graphs look like? What types of word problems can we solve with proportions?

Intro to ratios

• Intro to ratios (Opens a modal)
• Basic ratios (Opens a modal)
• Part:whole ratios (Opens a modal)
• Ratio review (Opens a modal)
• Basic ratios Get 5 of 7 questions to level up!

Visualize ratios

• Ratios with tape diagrams (Opens a modal)
• Equivalent ratio word problems (Opens a modal)
• Ratios and double number lines (Opens a modal)
• Ratios with tape diagrams Get 3 of 4 questions to level up!
• Equivalent ratios with equal groups Get 3 of 4 questions to level up!
• Create double number lines Get 3 of 4 questions to level up!
• Ratios with double number lines Get 3 of 4 questions to level up!
• Relate double number lines and ratio tables Get 3 of 4 questions to level up!

Equivalent ratios

• Ratio tables (Opens a modal)
• Solving ratio problems with tables (Opens a modal)
• Equivalent ratios (Opens a modal)
• Equivalent ratios: recipe (Opens a modal)
• Understanding equivalent ratios (Opens a modal)
• Ratio tables Get 3 of 4 questions to level up!
• Equivalent ratios Get 3 of 4 questions to level up!
• Equivalent ratio word problems Get 3 of 4 questions to level up!
• Equivalent ratios in the real world Get 3 of 4 questions to level up!
• Understand equivalent ratios in the real world Get 3 of 4 questions to level up!

Ratio application

• Ratios on coordinate plane (Opens a modal)
• Ratios and measurement (Opens a modal)
• Part to whole ratio word problem using tables (Opens a modal)
• Ratios on coordinate plane Get 3 of 4 questions to level up!
• Ratios and units of measurement Get 3 of 4 questions to level up!
• Part-part-whole ratios Get 3 of 4 questions to level up!

Intro to rates

• Intro to rates (Opens a modal)
• Solving unit rate problem (Opens a modal)
• Solving unit price problem (Opens a modal)
• Rate problems (Opens a modal)
• Comparing rates example (Opens a modal)
• Rate review (Opens a modal)
• Unit rates Get 5 of 7 questions to level up!
• Rate problems Get 3 of 4 questions to level up!
• Comparing rates Get 3 of 4 questions to level up!

HOW TO SOLVE RATIO WORD PROBLEMS

In this section, you will learn how word problems on ratio can be solved.

Let us look at the stuff which are required to solve word problems on ratio. 

For example,

If two persons A & B are earning $400 and $ 500 respectively per week, the ratio of their earnings is 

A : B  =  400 : 500

When we simplify, we get  

A : B  =  4 : 5

From the ratio 4:5, if we want to get the earning of A and B, we have to multiply the terms of the ratio  4 & 5 by 100.

From the above point, it is very clear that if we want to get original quantity from the ratio, we have to multiply both the terms of the ratio by the same number.

In the above problem, we know that we have to multiply by 100. In case, we do not know what number to be multiplied, we have to multiply by "x" or any alphabet.

For example, the ages of two persons are in the ratio 

Age of the 1st person  =  5x

Age of the 2nd person  =  6x

(The value of 'x' to be found)

If a quantity increases or decreases in the ratio a : b,  then new quantity is

= 'b' of the original quantity divided by 'a' 

new quantity  =  (b x original quantity) / a

Increment Ratio :

In a ratio, if the second term is greater than the first term, it is called increment ratio.

Examples:  7 : 8 , 4 : 5, 1 : 5.

Decrement Ratio :

In a ratio, if the second term is smaller than the first term, it is called decrement ratio.

Examples : 8 : 7, 4 : 3, 9 : 7.

How to find increment ratio :

A quantity called 'A' has been increased to '3A'.

Now, to find the ratio in which it has been increased, just take the coefficient of A in the changed quantity '3A'. It is '3'.

Now we have to write this '3' as a fraction. That is 3/1. From the fraction '3/1', we have to form a increment ratio. Because, the original quantity has been increased. 

Therefore, the increment ratio from '3/1' is 1 : 3.

How to find decrement ratio :

A quantity called 'A' has been decreased to '0.25A'.

Now, to find the ratio in which it has been decreased, just take the coefficient of A in the changed quantity '0.25A'. It is '0.25'.

Now we have to write this '0.25' as a fraction. That is '1/4'. From the fraction '1/4', we have to form a decrement ratio. Because, the original quantity has been decreased. 

Therefore, the decrement ratio from '1/4' is 

Let us see how the above explained stuff help us to solve the ratio word problem given below.

Find in what ratio, will the total wages of the workers of a factory be increased or decreased if there be a reduction in the number of workers in the ratio 15:11 and an increment in their wages in the ratio 22:25.

Let us understand the given information. There are two information given in the question. 

1. In a factory, there is a reduction in the number of workers in the ratio 15:11.

2. There is an increment in their wages in the ratio 22:25.

Target of the question :

In what ratio, will the total wages of the factory be increased or decreased ?

Let 'x' be the original number of workers 

Let 'y' be the wages per worker.

Total wages  =  (No. of workers) x (wages per worker)

Before the given two changes,

Total wages  =  xy  or  1xy

After reduction in the number of workers in the ratio

Number of workers in the factory is 

=  11x / 15   (see stuff 2)

After increment in wages in the ratio

Wages per worker is 

=  25y / 22   (see stuff 2)

After the two changes, 

Total wages  =  (11x/15) x (25y/22)

Total wages  =  (5/6)xy  =  (0.833)xy

Total wages  =  1xy  ----(1)

After the given two changes,

Total wages  =  (0.83)xy ----(2)

Comparing (1) and (2), it is very clear that total wages has been decreased when the two changes are applied.

That is, total wages has been decreased from  (1xy) to (0.83)xy

Now, to find the ratio in which it has been decreased, just take the coefficient of 'xy' in total wages after the two changes applied.

It is '0.83'.

Now we have to write this '0.83' as a fraction.

That is '5/6'.

From the fraction '5/6', we have to form a decrement ratio.

That is  '5 : 6' (See stuff 4).  

Therefore, the total wages of the factory will be decreased in the ratio

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here. 

Kindly mail your feedback to   [email protected]

We always appreciate your feedback.

© All rights reserved. onlinemath4all.com

• Sat Math Practice
• SAT Math Worksheets
• PEMDAS Rule
• BODMAS rule
• GEMDAS Order of Operations
• Math Calculators
• Transformations of Functions
• Order of rotational symmetry
• Lines of symmetry
• Compound Angles
• Quantitative Aptitude Tricks
• Trigonometric ratio table
• Word Problems
• Times Table Shortcuts
• 10th CBSE solution
• PSAT Math Preparation
• Privacy Policy
• Laws of Exponents

Recent Articles

How to Find the Vertex of a Parabola

May 12, 24 10:03 PM

Converting Between Polar and Rectangular Coordinates

May 12, 24 01:14 PM

Trigonometry Sum and Difference Identities

May 07, 24 09:17 AM

• Word Problems on Ratio

We will learn how to divide a quantity in a given ratio and its application in the word problems on ratio.

1. John weights 65.7 kg. If he reduces his weight in the ratio 5 : 4, find his reduced weight.

Let the previous weight be 5x.

x = \(\frac{65.7}{5}\)

Therefore, the reduce weight = 4 × 13.14 = 52.56 kg.

2. Robin leaves $ 1245500 behind. According to his wish, the money is to be divided between his son and daughter in the ratio 3 : 2. Find the sum received by his son.

We know if a quantity x is divided in the ratio a : b then the two parts are \(\frac{ax}{a + b}\) and \(\frac{bx}{a + b}\).

Therefore, the sum received by his son = \(\frac{3}{3 + 2}\) × $ 1245500  

= \(\frac{3}{5}\) × $ 1245500

= 3 × $ 249100

= $ 747300  

3. Two numbers are in the ratio 3 : 2. If 2 is added to the first and 6 is added to the second number, they are in the ratio 4 : 5. Find the numbers.

Let the numbers be 3x and 2x.

According to the problem,

\(\frac{3x + 2}{2x + 6}\) = \(\frac{4}{5}\)

⟹ 5(3x + 2) = 4

⟹ 15x + 10 = 8x + 24

⟹ 15x – 8x = 24 - 10

⟹ x = \(\frac{14}{7}\)

Therefore, the original numbers are: 3x = 3 × 2 = 6 and 2x = 2 × 2 = 4.

Thus, the numbers are 6 and 4.

4. If a quantity is divided in the ratio 5 : 7, the larger part is 84. Find the quantity.

Let the quantity be x.

Then the two parts will be \(\frac{5x}{5 + 7}\) and \(\frac{7x}{5 + 7}\).

Hence, the larger part is 84, we get

\(\frac{7x}{5 + 7}\) = 84

⟹ \(\frac{7x}{12}\) = 84

⟹ 7x = 84 × 12

⟹ 7x = 1008

⟹ x = \(\frac{1008}{7}\)

Therefore, the quantity is 144.

●  Ratio and proportion

• Basic Concept of Ratios
• Important Properties of Ratios
• Ratio in Lowest Term
• Types of Ratios
• Comparing Ratios
• Arranging Ratios
• Dividing into a Given Ratio
• Divide a Number into Three Parts in a Given Ratio
• Dividing a Quantity into Three Parts in a Given Ratio
• Problems on Ratio
• Worksheet on Ratio in Lowest Term
• Worksheet on Types of Ratios
• Worksheet on Comparison on Ratios
• Worksheet on Ratio of Two or More Quantities
• Worksheet on Dividing a Quantity in a Given Ratio
• Definition of Continued Proportion
• Mean and Third Proportional
• Word Problems on Proportion
• Worksheet on Proportion and Continued Proportion
• Worksheet on Mean Proportional
• Properties of Ratio and Proportion
• 10th Grade Math

From Word Problems on Ratio to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math . Use this Google Search to find what you need.

New! Comments

• Preschool Activities
• Kindergarten Math
• 1st Grade Math
• 2nd Grade Math
• 3rd Grade Math
• 4th Grade Math
• 5th Grade Math
• 6th Grade Math
• 7th Grade Math
• 8th Grade Math
• 9th Grade Math
• 11 & 12 Grade Math
• Concepts of Sets
• Probability
• Boolean Algebra
• Math Coloring Pages
• Multiplication Table
• Cool Maths Games
• Math Flash Cards
• Online Math Quiz
• Math Puzzles
• Binary System
• Math Dictionary
• Conversion Chart
• Homework Sheets
• Math Problem Ans
• Free Math Answers
• Printable Math Sheet
• Funny Math Answers
• Employment Test
• Math Patterns
• Link Partners
• Privacy Policy

Recent Articles

Numbers | Notation | Numeration | Numeral | Estimation | Examples

May 12, 24 06:28 PM

Face Value and Place Value|Difference Between Place Value & Face Value

May 12, 24 06:23 PM

Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns

May 12, 24 06:09 PM

Worksheet on Bar Graphs | Bar Graphs or Column Graphs | Graphing Bar

May 12, 24 04:59 PM

Worksheet on Pictographs | Picture Graph Worksheets | Pictograph Works

May 12, 24 04:31 PM

© and ™ math-only-math.com. All Rights Reserved. 2010 - 2024.