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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 : 7. Together they had 144 cards throughout. How many cards did Liam give to Noah?
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The pattern behind it: Constant total
Money moves between two people, so their total never changes.
In this one. Because the cards only move between Liam and Noah, the same total of 144 can be split using each 12-unit ratio.
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.
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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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