Grade: Grade 5 Subject: SAT/ACT Skills Unit: Ratios Introduction SAT: Problem Solving + Data Analysis ACT: Math

Ratio Word Problems

📖 Learn

Ratio word problems appear frequently on the SAT and ACT! In this lesson, you'll learn how to solve different types of ratio problems using strategies that will help you succeed on test day.

Types of Ratio Problems on Tests

On standardized tests, you'll encounter several types of ratio problems:

  • Finding equivalent ratios - Given one ratio, find another that equals it
  • Finding unknown values - One part of a ratio is missing
  • Scaling problems - Increasing or decreasing both parts of a ratio
  • Real-world applications - Recipes, maps, mixtures, and more

Finding Equivalent Ratios

Two ratios are equivalent if they represent the same relationship. You can create equivalent ratios by multiplying or dividing both parts by the same number.

The Golden Rule of Equivalent Ratios

Whatever you do to one part of a ratio, you must do to the other part!

  • 2:3 becomes 4:6 (multiplied both by 2)
  • 2:3 becomes 6:9 (multiplied both by 3)
  • 8:12 becomes 2:3 (divided both by 4)
📊 Equivalent Ratio Table Generator
Start ratio: :
Multiplier First Number Second Number Ratio

Using Ratio Tables to Find Unknown Values

A ratio table helps you organize information and find patterns. When you know one value, you can use the table to find the missing value.

Test-Taking Tip: When you see a ratio problem on the SAT or ACT, draw a quick ratio table to organize your work. It helps you avoid mistakes and shows your reasoning!

Setting Up and Solving Ratio Word Problems

Follow these steps to tackle any ratio word problem:

RATIO Problem-Solving Strategy

R Read carefully - What two things are you comparing? Identify the quantities.
A Arrange the ratio - Write the ratio in the correct order. The order matters!
T Think about what you need to find - What value is unknown? What do you know?
I Identify the multiplier - What number connects the known values to find the unknown?
O Output your answer with units - Always include units in your final answer!

💡 Examples

Let's work through three ratio word problems step by step, using multiple solution methods.

1 The Animal Shelter Problem
The ratio of dogs to cats at the shelter is 3:5. If there are 15 cats, how many dogs are there?

Method 1: Using a Ratio Table

1
Set up the ratio table

Dogs : Cats = 3 : 5

DogsCats
35
?15
2
Find the multiplier

What number times 5 equals 15?

5 x ? = 15
5 x 3 = 15

The multiplier is 3.

3
Apply the same multiplier to find dogs
3 x 3 = 9
✓ There are 9 dogs at the shelter.
Alternative Method: Using Proportions

You can also set up and solve a proportion:

3/5 = x/15

Cross multiply: 5 x X = 3 x 15

5x = 45
x = 9 dogs
2 The Recipe Problem
A cookie recipe uses flour and sugar in the ratio 4:1. If you want to use 2 cups of sugar, how many cups of flour do you need?
1
Read and arrange the ratio

Flour : Sugar = 4 : 1

We know sugar = 2 cups, and we need to find flour.

2
Find the multiplier

Original sugar = 1, New sugar = 2

1 x 2 = 2

The multiplier is 2.

3
Apply the multiplier to flour
4 x 2 = 8
✓ You need 8 cups of flour.
3 The Map Scale Problem
On a map, 2 centimeters represents 5 kilometers. If two cities are 8 centimeters apart on the map, what is the actual distance between them?
1
Set up the ratio

Map distance : Actual distance = 2 cm : 5 km

2
Find the multiplier

Map distance changes from 2 cm to 8 cm

2 x ? = 8
2 x 4 = 8

The multiplier is 4.

3
Apply the multiplier to find actual distance
5 x 4 = 20
✓ The actual distance is 20 kilometers.
Checking Your Work

Always verify! The ratios should be equivalent:

2:5 = 8:20

Both simplify to the same ratio when divided by their GCF.

8 / 4 = 2 and 20 / 4 = 5 ✓

✏️ Practice

Try these ratio word problems on your own. Use the RATIO strategy and check your answers!

1 Recipe
A lemonade recipe uses water and lemon juice in the ratio 6:1. If you use 3 cups of lemon juice, how many cups of water do you need?
cups of water
2 Map Scale
On a map, the scale is 3 inches to 12 miles. If two locations are 9 inches apart on the map, what is the actual distance in miles?
miles
3 Mixture
To make purple paint, you mix red and blue paint in the ratio 2:5. If you use 10 tablespoons of blue paint, how many tablespoons of red paint do you need?
tablespoons of red
4 Real World
At summer camp, the ratio of counselors to campers must be 1:8. If there are 56 campers, how many counselors are needed?
counselors

✅ Check Your Understanding

Test your mastery with the Ratio Champion challenge! Answer 6 progressively harder questions to prove your skills.

🏆 Ratio Champion
Score: 0/6 Question: 1/6

Loading question...

What is your answer?

Key Concepts Summary

📐 Equivalent Ratios

Multiply or divide both parts by the same number to create equivalent ratios.

📊 Ratio Tables

Organize your work in a table to find patterns and avoid mistakes.

🔢 Finding Multipliers

Divide the known values to find what number connects them.

✓ Check Your Work

Verify that your ratios are equivalent by simplifying both.

🎯 Remember the RATIO Strategy

  • Read carefully - identify what you're comparing
  • Arrange the ratio in the correct order
  • Think about what you need to find
  • Identify the multiplier between known values
  • Output your answer with units

🚀 Next Steps

  • Practice more ratio problems with different contexts (recipes, maps, mixtures)
  • Look for ratios in your daily life - recipes, sports statistics, and more!
  • Challenge yourself with multi-step ratio problems
  • Review equivalent fractions - they work the same way as ratios!
SAT/ACT Tip: On test day, always write down your work! Drawing a quick ratio table takes seconds and helps you avoid careless errors. Plus, if you need to check your work, you can easily see your steps.