Question P6 Everything changed
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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?
Answer
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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.
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.
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.
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