AlgebraHardHeads and legs
Algebra practice question
A farmer keeps chickens and cows. Together the animals have 20 heads and 56 legs. How many cows are there?
Answer: 8
Let c be chickens and w cows: c + w = 20 and 2c + 4w = 56. Substitute c = 20 − w: 40 − 2w + 4w = 56, so 2w = 16 and w = 8. Check: 12 chickens (24 legs) + 8 cows (32 legs) = 56.
Common wrong answers
- If you answered 12
- 12 is the number of CHICKENS.
- If you answered 14
- 14 is 56/4, as if every animal were a cow — but then there would be only 14 heads.
- If you answered 28
- 28 is 56/2, as if every animal were a chicken.
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