A medium question on chickens and rabbits for P3–P4, with a step-by-step solution, diagrams and the answer. One of the best-known Olympiad problem types: in the Hua Xia Cup it appears from the P2 first round to the P5 papers.
The question
In a cage on a farm there are chickens and rabbits, with 2 more chickens than rabbits.
Each chicken has 2 legs and each rabbit has 4; there are 40 legs in all.
How many rabbits are there?
Show the hints (2)
💡Hint 1: Take away the 2 extra chickens first. How do the rest compare?
💡Hint 2: Then there are as many of each. A pair of one of each has how many legs?
Worked solution
Have a go first, then read the solution step by step.
1.First take away the 2 extra chickens. They have 2 × 2 = 4 legs.
2.That leaves 40 − 4 = 36 legs, and now there are as many of each.
3.Put one chicken and one rabbit together as a pair: 2 + 4 = 6 legs.
4.36 ÷ 6 = 6 pairs. Each pair has one rabbit, so there are 6 rabbits.
⚠️Common mistake: taking away just 2, forgetting each has 2 legs.
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