The average mass of a basket of apples is 150 g. When one more apple with a mass of 330 g is added into the basket, the average mass of the apples becomes 170 g. How many apples are there in the basket at first?
Need a hint?
The new apple is heavier than the old average. Think about how much 'extra' mass it brings and how that extra mass raises every apple's average.
Worked answer
- The new apple has a mass of 330 g, but the new average is 170 g.
- So the new apple brings 330 − 170 = 160 g more than the new average.
- This extra 160 g raises each of the apples at first from 150 g to 170 g, which is 170 − 150 = 20 g each.
- Number of apples at first = 160 ÷ 20 = 8.
- Check: 8 × 150 = 1200 g, 1200 + 330 = 1530 g, 1530 ÷ 9 = 170 g.
- Answer: 8 apples.
The mistake this question tests
Average and total
Pupils often just divide 330 by 170 or by 150, or subtract the averages (170 − 150 = 20) and stop, not knowing what to do next. The key is to compare totals, not averages alone.
How to fix it at home →Wrong answers children often give:
- 9 Average and total
- 20 Average and total
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See the answer →Practise PSLE whole numbers until the mistakes stop.
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