Applications and Problem Solving

1-5Translating Sentences into Equations

Overview

‘Is,’ ‘equals,’ ‘the result is’ all mean ‘=’. Turn the words into an equation, then solve.

Key ideas

  • Identify the unknown and assign a variable.
  • Write the relationship as an equation.
  • Check your equation against the sentence.

Worked examples

Example 1

Problem. ‘The sum of x and 12 is 30.’

Solution. x + 12 = 30, so x = 18

Example 2

Problem. ‘Twice n decreased by 5 equals 11.’

Solution. 2n − 5 = 11, so n = 8

Practice

Try each one. Click Show answer when ready.

  1. 1.

    ‘Three times y is 27.’ Write and solve.

  2. 2.

    ‘x increased by 4 equals 19.’

  3. 3.

    ‘5 less than 2n is 13.’

Challenge problems

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

  1. 1.

    Translate: Three times a number decreased by 7 is equal to twice the number increased by 5.

  2. 2.

    Translate: The sum of two consecutive integers is 47.