Module 2 of 6 · MA4-EQU-C-01

Word problems

Translate word problems into equations and solve them

01

Name the unknown first

Write 'Let x be the number of…' before anything else. Half the marks in a word problem come from defining the pronumeral and writing a correct equation, even if the arithmetic then goes wrong.

02

Translate phrase by phrase

'5 more than three times a number' is 3x + 5. Work left to right through the sentence and write each phrase as you meet it. 'Is' or 'gives' or 'equals' becomes the = sign.

03

Watch the order in subtraction

'7 less than x' is x − 7, not 7 − x. The thing you subtract is the number that comes *before* 'less than'. This trap appears in almost every test.

04

Answer the question that was asked

If x was the number of adult tickets, and the question asked for the number of child tickets, you have one more step to do after solving. Finish with a sentence, not a bare number.

The rules to know by heart

  • Sum / total / altogethermeans add (+)
  • Difference / less than / fewermeans subtract (−), and the order flips
  • Product / times / ofmeans multiply (×)
  • Quotient / shared / permeans divide (÷)
  • Is / gives / results inmeans equals (=)

See it work

Try it — build the equation, don't solve it

7 less than 3 times a number is 26.

Let x be the number.

Tap tiles to build it here…

A worked example

I think of a number, multiply it by 4, then subtract 18. The result is -2. What was my number?

Worked solution

  1. Let x be the number.(always name the unknown first)
4 to go

Every line has its reason in brackets. In the test, that bracket is worth marks on its own — write it even when the number feels obvious.

ready?

Practise until you get five in a row.

MA4-EQU-C-01 · NSW Mathematics K–10 (2022)