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Nadia and Priya's beads — what Nadia gave
In a craft class, the ratio of Nadia's beads to Priya's beads was 4 : 1. After Nadia gave some of her beads to Priya, the ratio became 3 : 2. Together they had 150 beads throughout. How many beads did Nadia give to Priya?
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Nadia gave Priya 30 beads. Check: at first they had 120 and 30 beads, so the ratio was 4 : 1 and the total w…
The pattern behind it: Constant total
Money moves between two people, so their total never changes.
In this one. The beads only move between Nadia and Priya, so the same total of 150 can be split using each ratio in turn.
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.