How to Solve Ratio Word Problems

Ratio word problems compare quantities. The trick is keeping the order of the comparison consistent from start to finish.

Quick idea

Set up the ratio in the same order as the words, then scale both parts by the same factor.

Steps

1. Identify the two quantities being compared.
2. Write the ratio in the stated order.
3. Use scaling, a ratio table, or a proportion.
4. Answer the exact question being asked.

Worked example

The ratio of boys to girls is 2 to 3. If there are 10 boys, how many girls are there?

Full solution

Step-by-step walkthrough

Step 1

Boys go from 2 to 10, which is times 5.

Step 2

Girls must also be multiplied by 5.

Step 3

Three times 5 equals 15 girls.

Common mistake

Do not reverse the ratio halfway through. Boys to girls and girls to boys are different comparisons.

Practice problems

1. A ratio is 1:4. If the first part is 3, find the second.
2. A class has red to blue pencils 5:2. If red is 20, find blue.
3. Simplify a ratio of 12 wins to 8 losses.

Answers

1. 12
2. 8
3. 3:2

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Solve Ratio Problems
• How to Solve Proportions
• Similar Triangles Explained