Chapter 6.3, Problem 15P

A farm raises a total of 220 chickens and pigs. The number of legs of the stock in the farm totals 520. How many chickens and pigs are at the farm?

To determine

To find: The number of chickens and pigs in the farm

Answer to Problem 15P

The number of chickens in the farm is 180.

The number of pigs in the farm is 40.

Explanation of Solution

Given information:

A farm raises a total 220 chickens and pigs.

The number of legs of the stock in the farm is 520.

Calculation:

Let the number of chickens in the farm = $x$

Let the number of pigs in the farm = $y$

According to the first condition:

$x+y=220$

Number of legs of a chicken =2

Number of legs of a pig =4

According to the second condition:

$2x+4y=520$

In order to solve these equations, we use elimination method:

$\left[\begin{array}{c}x+y=220\\ 2x+4y=520\end{array}\right]$

Multiply $x+y=220\text{by}2:2x+2y=440$

$\left[\begin{array}{c}2x+2y=440\\ 2x+4y=520\end{array}\right]$

$\begin{array}{l}2x+4y=520\\ -\\ \underset{\_}{2x+2y=440}\\ 2y=80\end{array}$

$\left[\begin{array}{c}2x+2y=440\\ 2y=80\end{array}\right]$

Solve $2y=80\text{for}y:$

$2y=80$

Divide both sides by 2:

$\frac{2y}{2}=\frac{80}{2}$

Simplify:

$y=40$

Now plug $y=40$ in $2x+2y=440$ :

$2x+2\cdot 40=440$

$2x+80=440$

Subtract 80 from both sides:

  $2x+80-80=440-80$

Simplify:

$2x=360$

Divide both sides by 2:

$\frac{2x}{2}=\frac{360}{2}$

$x=180$

Therefore, the number of chickens in the farm is 180.

The number of pigs in the farm is 40.