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.
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
- Let x be the number.(always name the unknown first)
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.