An easy question on ratios for P5, with a step-by-step solution, diagrams and the answer. Ratio questions appear in the Hua Xia Cup's P4 to P6 first rounds, qualifying rounds and finals, such as linked ratios and ratios that change.
The question
The school library has bought a batch of new Chinese and English books.
The numbers of Chinese and English books are in the ratio 3 :
1, and there are 38 more Chinese books than English ones.
How many Chinese books are there?
Show the hints (2)
💡Hint 1: Think in equal parts: how many more parts are the Chinese books than the English books?
💡Hint 2: Those extra parts are the 38 extra.
Worked solution
Have a go first, then read the solution step by step.
1.The Chinese books are 3 parts and the English books 1 part. Lined up, that is 3 − 1 = 2 parts more.
2.Those 2 parts are the 38 extra: 1 part = 38 ÷ 2 = 19.
3.The Chinese books are 3 parts: 3 × 19 = 57.
⚠️Common mistake: working out 38 ÷ 3. The 38 extra is only 2 parts.
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