AlgebraStructure & Method · Book 1All Chapters

Applications and Problem Solving

1-6Translating Problems into Equations

Overview

Use a five-step plan: read carefully, label the unknown, write an equation, solve, check against the original problem.

Key ideas

  • Underline what you know and what you need to find.
  • Let a variable stand for the unknown quantity.
  • Write a sentence that becomes the equation.

Worked examples

Example 1

Problem. A number plus 17 equals 40. Find the number.

Solution. Let x be the number. x + 17 = 40 → x = 23.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Three more than a number equals 21. Find it.

  2. 2.

    Half of a number is 16. Find it.

  3. 3.

    Twice a number, minus 4, is 26. Find it.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Set up an equation: A rectangle's length is 3 cm more than its width. The perimeter is 38 cm. Find the dimensions.

  2. 2.

    Set up an equation: There are 32 coins in nickels and quarters worth $4.40. How many of each?