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.
‘Three times y is 27.’ Write and solve.
- 2.
‘x increased by 4 equals 19.’
- 3.
‘5 less than 2n is 13.’
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Translate: Three times a number decreased by 7 is equal to twice the number increased by 5.
- 2.
Translate: The sum of two consecutive integers is 47.