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Sara and Tom's savings — what Sara gave
The ratio of Sara's savings to her brother Tom's savings was 5 : 1. After Sara gave some of her savings to Tom, the ratio became 2 : 1. Together they had $180 throughout. How much money did Sara give to Tom?
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The pattern behind it: Constant total
Money moves between two people, so their total never changes.
In this one. The money only moves between Sara and Tom, so the unchanged $180 total can be split by each ratio in turn to find the real amounts before and after.
How to spot it
One person gives, sells or loses an amount to the other, and nobody outside the two people gains or loses anything.
Common mistake
Children draw different totals before and after, or forget that moving an amount from one person to the other changes the gap between them by twice that amount.
Try one like it
Standard Liam and Noah's cards — 7 : 5 becomes 5 : 7 The ratio of Liam's trading cards to Noah's trading cards was 7 : 5. After Liam gave some of his cards to Noah, the ratio became 5…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.
A PDF, and a note when new solutions go up.