Today’s problem — free all day, every step. Every day has one.
Cookies — Box A and Box B swap
The ratio of cookies in Box A to cookies in Box B was 5 : 3. After 16 cookies were moved from Box A to Box B, the ratio became 3 : 5. How many cookies were in Box A at first?
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65 worked examples are free without a code, two from every pattern. No account, either way.
The pattern behind it: Constant total
Money moves between two people, so their total never changes.
In this one. Both ratios add up to 8 shares, and no cookies entered or left, so the total is the same 8 shares before and after — which forces 1 part (after) to be exactly 1 unit (before), and the 16 cookies to be exactly 2 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.