At a beach clean-up, 31 volunteers each collected either 1, 2 or 3 bags. The number of volunteers who collected 1 bag to the number who collected 2 bags was 2 : 3. Altogether, the volunteers collected 65 bags.
- Find the number of volunteers who collected 2 bags.
Need a hint?
Make a group of 2 volunteers who collected 1 bag and 3 who collected 2 bags. Then imagine every volunteer collected 3 bags and compare with 65.
Worked answer
- For every 2 volunteers who collected 1 bag, there were 3 who collected 2 bags. Call these 5 volunteers one group.
- One group collects 2 × 1 + 3 × 2 = 8 bags.
- If all 31 volunteers had collected 3 bags, there would be 31 × 3 = 93 bags.
- That is 93 − 65 = 28 bags too many.
- One group collects 5 × 3 − 8 = 7 bags fewer than 5 volunteers who each collect 3 bags.
- Number of groups = 28 ÷ 7 = 4.
- Volunteers who collected 2 bags = 4 × 3 = 12.
The mistake this question tests
Stopped at one part in ratio
A common mistake is to treat the ratio 2 : 3 as the actual numbers of volunteers. The ratio gives only the relative sizes of the two groups, and some volunteers also collected 3 bags.
How to fix it at home →Wrong answers children often give:
- 3 Stopped at one part in ratio
More PSLE ratio questions
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See the answer →Practise PSLE ratio until the mistakes stop.
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