How to Turn Word Problems Into Equations

Turning words into equations is the bridge between arithmetic and algebra. Once the equation is correct, solving is usually straightforward.

Quick idea

Define the unknown, translate the relationship, and keep the equal sign where the story says two quantities match.

Steps

1. Choose a variable for the unknown quantity.
2. Translate phrases like increased by, twice, difference, and total.
3. Build an equation around the relationship in the story.
4. Solve and check the answer in the original sentence.

Worked example

A number doubled plus 5 is 17. Find the number.

Full solution

Step-by-step walkthrough

Step 1

Let x be the unknown number.

Step 2

Doubled means 2x, and plus 5 means add 5.

Step 3

Solve the equation to get x equals 6.

Common mistake

Do not put the equal sign wherever the word is appears without reading the whole sentence. The equal sign separates two quantities that have the same value.

Practice problems

1. Five more than a number is 13.
2. Three times a number is 21.
3. A number decreased by 4 is 10.

Answers

1. x + 5 = 13, x = 8
2. 3x = 21, x = 7
3. x - 4 = 10, x = 14

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 One-Step Equations
• How to Solve Two-Step Equations
• How to Solve Math Word Problems