Today’s problem — free all day, every step. Every day has one.
Car park — cars and motorcycles, counting wheels
A car park has 14 vehicles, only cars and motorcycles. Each car has 4 wheels and each motorcycle has 2 wheels. In total there are 40 wheels. How many cars are there?
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There are 6 cars and 8 motorcycles. Check: 6 + 8 = 14 vehicles and 6 × 4 + 8 × 2 = 24 + 16 = 40 wheels, so e…
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. Changing one motorcycle into one car keeps the vehicle count fixed but adds exactly 2 wheels, so the number of changes is the wheel shortfall divided by 2.
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.