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Chickens and cows — 32 legs
On a small farm there are 10 animals, a mix of chickens and cows. Each chicken has 2 legs and each cow has 4 legs. Together the animals have 32 legs. How many cows 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. Suppose every animal is the one with fewer legs, measure the shortfall that leaves, then divide by what a single swap gains — the number of swaps is the number of cows.
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.