Question

A farm raises a total of 220 animals that are chickens and pigs. The number of legs of stock in the farm total 520. How many chickens and how many pigs? Label variables, write a system of equations and solve

Answer 1

Let:
- \( c \) = the number of chickens
- \( p \) = the number of pigs

We have the following information:

1. The total number of animals (chickens and pigs) is 220:
\[
c + p = 220
\]

2. Chickens have 2 legs each and pigs have 4 legs each, and the total number of legs is 520:
\[
2c + 4p = 520
\]

We now have a system of equations to solve:

1. \( c + p = 220 \) (Equation 1)
2. \( 2c + 4p = 520 \) (Equation 2)

**Step 1: Simplify Equation 2.**

Divide Equation 2 by 2:
\[
c + 2p = 260 \tag{Equation 3}
\]

**Step 2: Solve the system of equations using substitution or elimination.**

We can substitute Equation 1 into Equation 3. From Equation 1, we can express \( c \) in terms of \( p \):
\[
c = 220 - p
\]

Now, substitute this into Equation 3:
\[
(220 - p) + 2p = 260
\]
\[
220 + p = 260
\]
\[
p = 260 - 220
\]
\[
p = 40
\]

**Step 3: Substitute \( p \) back to find \( c \).**

Using Equation 1:
\[
c + 40 = 220
\]
\[
c = 220 - 40
\]
\[
c = 180
\]

**Final Solution:**

The number of chickens is \( c = 180 \) and the number of pigs is \( p = 40 \).

Thus:
- Number of chickens: **180**
- Number of pigs: **40**