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Mrs Tan and Mrs Lee's stamps — 2 : 1 to 4 : 1
The number of stamps Mrs Tan owned to the number Mrs Lee owned was in the ratio 2 : 1. After Mrs Tan received another 180 stamps and Mrs Lee gave away 60 stamps to her nephew, the ratio became 4 : 1. How many stamps did Mrs Tan own at first?
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The pattern behind it: Everything changed
Both amounts change, so no total and no gap stays fixed.
In this one. Mrs Tan's stamps in the end can be written two ways — 2u + 180 from her own gain, and 4(u − 60) from the end ratio — and setting the two equal is what pins down one unit.
How to spot it
Both people in a ratio change by different amounts, with words like 'joined' or 'saved more' for one and 'left' or 'spent' for the other.
Common mistake
Children look for a fixed total or a fixed gap out of habit. Neither is fixed here, so only the ratio at the end can give the size of a share.
Try one like it
Challenging Ali and Billy — 2 : 1 becomes 4 : 1 The ratio of Ali’s money to Billy’s money was 2 : 1. After Ali saved another $60 and Billy spent $150, the ratio became 4 : 1. How…The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
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