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Water bottles on a hike — adults and children
On a hiking trip, there are 70 bottles of water for 65 hikers, made up of adults and children. Each adult drinks 3 bottles of water, and every 2 children share 1 bottle. How many adults and how many children are on the hike?
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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. Guess that everyone is one kind, then swap one for the other: each swap changes the total by a fixed amount, so shortfall ÷ change per swap tells you how many to swap.
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.