Question

There are 22 animals in the barn. Some are chickens and some are pigs. There are 74 legs in all. How many of each animal are there?

Answer 1

To solve this, set up a system of equations and then solve for each variable.

There are 22 animals. Some are pigs (p) and some are chickens (c) This gives us this equation: p + c = 22. The total of all the pigs + all of the chickens in the barn is 22 animals

There are 74 legs in total. Chickens have 2 legs and pigs have 4 legs. This leads to this equation: 2c + 4p = 74. The total of all the chickens legs + all the pigs legs = 74

I am now going to solve this by substitution. If p + c = 22, than p = 22 - c. I can substitute that for p in the second equation to solve for the amount of chickens.

2c + 4(22 - c) = 74
2c + 88 -4c = 74
-2c = -14
c = 7

Knowing that c = 7, I can plug 7 into the original equation to solve for p.
p + c = 22
p + 7 = 22
p = 15

There are 7 chickens and 15 pigs. To check my work, you can plug 7 and 15 into the second equation and make sure both sides equal each other.

Answer 2

We could make an expression.

74=2c+4p

A possibility is 7 chickens and 15 pigs.

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hope it helps