Question

A farmer has both sheep and chickens on his farm. All the animals have the expected number of parts. When his animals are all

Answer 1

Answer:

13 sheep, 19 chicken

Step-by-step explanation:

You can start to solve this problem by assigning variables. First, let's assign the number of sheep there are as $x$ and the number of chickens there are as $y$.

Because each sheep has 4 legs, the number of legs for each sheep would be $4x$. Similarly, because each chicken has 2 legs, the number of legs for each chicken would be $2y$. Each animal would have 1 head, so the number of heads would just be $x$ and $y$. Because the number of legs in total are 90, $4x + 2y=90$. Because the number of heads in total are 32, $x+y=32.$

There is now a system of equations with two unknown variables and two equations. There are many ways to solve this, but for me, the easiest would be elimination. First, I would double the second equation, $2x+2y=64$. Then, I would subtract that from the first equation, eliminating $y$. $2x=26$. Solving for x gives 13. We can then plug that value into the second equation, making y be $32-13=19$. This means that $x=13$ and $y=19$, meaning that there are 13 sheep and 19 chicken.