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Marbles — Marcus and Ben's game
The ratio of Marcus's marble collection to Ben's marble collection was 3:2. After Marcus won 24 more marbles and Ben lost 9 marbles in a game, the new ratio became 3:1. How many marbles did Marcus have 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. Keep one original-ratio unit as an unknown u; because both amounts changed, use the final 3:1 relationship between 3u+24 and 2u-9 to determine u.
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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