Solving Problems

3-4Using Equations to Solve Problems

Overview

Translate a real-world situation into an equation, solve it, and interpret the result.

Key ideas

  • Define the variable clearly.
  • Write one equation that captures the problem.
  • Check your answer in the original context.

Worked examples

Example 1

Problem. A number doubled and increased by 7 is 31. Find it.

Solution. 2n + 7 = 31 → 2n = 24 → n = 12.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    5 more than 3 times a number is 26.

  2. 2.

    If 8 is subtracted from twice a number, the result is 14.

  3. 3.

    One third of a number, increased by 4, equals 10.

Challenge problems

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

  1. 1.

    A number divided by 3, minus 4, equals 5. Find the number.

  2. 2.

    Twice a number plus 7 is the same as the number plus 15. Find the number.