Question P4–P5–P6 Suppose and swap
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A cycling club has 25 vehicles parked outside, a mix of bicycles and tricycles. Bicycles have 2 wheels and tricycles have 3 wheels. Altogether there are 58 wheels. How many tricycles are there?
Answer
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Suppose everything is one kind, then swap one at a time until the total is right.
In this one. Pretend every vehicle is the 2-wheel kind, see how many wheels you fall short by, and divide that shortfall by the 1 wheel each swap adds — the answer is how many tricycles there are.
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.
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.
Worked examples of all 33 patterns and skills, in a booklet you can print.