Question

a farmer saw some chickens and pigs in a field. he counted 60 heads and 176 legs. determine exactly how many chickens and pigs he saw.

Answer 1

32 chickens and 28 pigs

Explanation:

This is a solve the system question. Call C the number of chickens and P the number of pigs. Each chicken and each pig has one head so the first equation is:

`C+P=60`

Each chicken has 2 legs and each pig has 4 legs so the second equation is:

`2C+4P=176`

To solve by substitution, first rearrange the first equation to isolate C:

`C=60-P`

Now substitute that into the second equation and solve for P:

`2(60-P)+4P=176\\120-2P+4P=176\\2P=56\\P=28`

So there are 28 pigs. Now sub that into either of the original equations. I'll use the first:

`C+28=60\\C=32`

There are 32 chickens.