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Fried noodles — 80 people sharing 85 plates
There are 85 plates of fried noodles for 80 people. Each adult eats 2 plates and every 3 children share 1 plate. How many adults and how many children are there?
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The pattern behind it: Suppose and swap
Suppose everything is one kind, then swap one at a time until the total is right.
In this one. Count in thirds of a plate so every amount is a whole number — then suppose all 80 are children and swap them into adults one at a time, each swap adding exactly 6 − 1 = 5 thirds.
How to spot it
Two kinds of thing are mixed together with a known total count and a known total of something else, such as legs or sweets, and neither kind's count is given on its own.
Common mistake
Children lose track of whether a swap adds to the total or takes away from it. Compare the starting total with the target first, then swap in the direction that closes the gap.
Try one like it
Standard Bicycles and tricycles — 58 wheels A cycling club has 25 vehicles parked outside, a mix of bicycles and tricycles. Bicycles have 2 wheels and tricycles have 3 wheels…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.