A group of people, cats, and birds has seventy legs, thirty heads, and twenty
A group of people, cats, and birds has seventy legs, thirty heads, and twenty
tails. How many cats are among this group? (Assume all birds have two legs and a tail.)
Answer/Solution
5
Steps/Work
Write P, C, and B for the number of people, cats, and birds respectively, so that
we have
2P + 4C + 2B = 70; P + C + B = 30; C + B = 20:
Comparing the last two equations we obtain P = 10, and the rst equation simplies to
4C + 2B = 50, or 2C + B = 25. Therefore,
C = (2C + B) / (C + B) = 25 / 5 = 5:
Alternatively,
C = 1
2
2P + 4C + 2B
P + C + B
= 35 - 30 = 5:
correct answer B
we have
2P + 4C + 2B = 70; P + C + B = 30; C + B = 20:
Comparing the last two equations we obtain P = 10, and the rst equation simplies to
4C + 2B = 50, or 2C + B = 25. Therefore,
C = (2C + B) / (C + B) = 25 / 5 = 5:
Alternatively,
C = 1
2
2P + 4C + 2B
P + C + B
= 35 - 30 = 5:
correct answer B