A pottery studio had clay bowls and clay vases in the ratio 4 : 7 at first. It sold 12 bowls and then made 14 more vases. After this, the ratio of the number of bowls to the number of vases became 1 : 3.
- How many bowls were left after the sale?
- How many vases were there after the 14 new vases were made?
- How many pieces were there altogether at first?
Need a hint?
Work backwards from the new ratio. Find the bowls left, then the vases after making more, then add back what was sold and subtract what was made.
Worked answer
- (a) At first, bowls = 4 units and vases = 7 units.
- (a) After the changes, bowls = 4 units − 12 and vases = 7 units + 14.
- (a) Vases are 3 times the bowls: 7 units + 14 = 3 × (4 units − 12) = 12 units − 36.
- (a) 5 units = 14 + 36 = 50, so 1 unit = 10. Bowls left = 40 − 12 = 28.
- (b) Vases after = 3 × 28 = 84.
- (c) At first: bowls 40 and vases 70. Total = 40 + 70 = 110.
The mistake this question tests
Calculation slip
Pupils often apply the new ratio to the number of bowls at first, or add the 14 vases instead of subtracting them when working backwards from the after-amount.
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See the answer →Practise PSLE ratio until the mistakes stop.
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