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Marbles — Ravi, Suresh and Tara end up equal
Ravi, Suresh and Tara shared some marbles. Ravi had of the total, Suresh had 40% as many as Tara, and Tara gave 82 marbles to the other two so that all three had equal amounts. Find the original total number of marbles.
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The pattern behind it: Constant total
Money moves between two people, so their total never changes.
In this one. Scale the combined 49-unit ratio by 3 so its 147-unit total divides exactly into three equal final shares of 49 units.
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.