Question P4–P5–P6 Suppose and swap
Today’s problem — free all day, every step. Every day has one.
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?
Answer
There are 6 cars and 8 motorcycles. Check: 6 + 8 = 14 vehicles and 6 × 4 + 8 × 2 = 24 + 16 = 40 wheels, so every condition is satisfied.
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.
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.