Class 6B had 24 more pupils than Class 6A on a school camp. 25 of the pupils in Class 6A and 16 of the pupils in Class 6B brought a raincoat. The number of pupils who did not bring a raincoat was 3 times the number of pupils who did.
- What fraction of all the pupils on the camp brought a raincoat?
- How many pupils did not bring a raincoat?
Need a hint?
First find what fraction of all the pupils brought a raincoat. Then write that fraction of each class and compare it with the fractions in the question.
Worked answer
- (a) Pupils without a raincoat are 3 times those with one, so the total is 1 + 3 = 4 parts. Pupils with a raincoat are 14 of all the pupils.
- (b) Raincoat pupils = 25 of 6A + 16 of 6B = 14 of 6A + 14 of 6B.
- Move the 6A parts together: 25 − 14 = 320 of 6A. Move the 6B parts together: 14 − 16 = 112 of 6B.
- So 320 of 6A = 112 of 6B. Change both to sixtieths: 960 of 6A = 560 of 6B, so 6A : 6B = 5 : 9.
- 6B has 9 − 5 = 4 units more than 6A, and 4 units = 24 pupils, so 1 unit = 6 pupils.
- 6A = 5 × 6 = 30 pupils and 6B = 9 × 6 = 54 pupils, so the total is 84 pupils.
- Check: 25 of 30 = 12 and 16 of 54 = 9, so 21 pupils brought a raincoat, which is 14 of 84.
- Pupils who did not bring a raincoat = 84 − 21 = 63.
The mistake this question tests
Stopped at one part in ratio
Many pupils think 14 of each class brought a raincoat. The fractions are different for the two classes, so the classes cannot be treated in the same way.
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See the answer →Practise PSLE fractions until the mistakes stop.
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