Question

There are 40 pigs and chickens in a farmyard. Joseph counted 100 legs in all. How many pigs and how many chickens are there?

Answer 1

Explanation:

Solution 1: Let’s say P is the amount of pigs, and C is the amount of chickens. Since each pig has 4 legs, There are a total of 4P legs contributed by the pigs. Similarity, there are 2C legs contributed by the chickens. For the second sentence, there are a total of 40 chickens and pigs, meaning that P+C=40. Setting up equations,

P+C=40
4P+2C=100.

Solving these equations, there are 10 pigs, and 30 chickens.

Solution 2: Assume that all of the farm animals are chickens. There are a total of 80 legs counted. Now, we are 20 legs short. If we were to replace a chicken with a pig, we lose 2 legs from removing the chicken, but gain four legs from the pig, gaining a total of 2 legs. So if we were to add 10 pigs, there would be 100 legs. Once again, there are 10 pigs and 30 chickens.