Question

In a zoo, there are some parrots and some turtles. They have 40 heads and 124 feet. How many parrots and turtles are there in the zoo?

Answer 1

Let \( p \) be the number of parrots and \( t \) be the number of turtles.

We can set up the following equations based on the information given:

1. Each parrot and turtle has one head, so:
\[
p + t = 40
\]

2. Parrots have 2 feet each and turtles have 4 feet each, so:
\[
2p + 4t = 124
\]

Now, we can simplify the second equation. Dividing the entire equation by 2 gives us:
\[
p + 2t = 62
\]

We now have a system of equations:
1. \( p + t = 40 \) (Equation 1)
2. \( p + 2t = 62 \) (Equation 2)

Next, we will solve these equations. We can subtract Equation 1 from Equation 2:
\[
(p + 2t) - (p + t) = 62 - 40
\]
This simplifies to:
\[
t = 22
\]

Now that we have \( t \), we can substitute it back into Equation 1 to find \( p \):
\[
p + 22 = 40
\]
\[
p = 40 - 22 = 18
\]

Therefore, the number of parrots and turtles is:
\[
\text{Number of parrots } (p) = 18
\]
\[
\text{Number of turtles } (t) = 22
\]

We can check our work:
- Total heads: \( 18 + 22 = 40 \) (correct)
- Total feet: \( 2 \times 18 + 4 \times 22 = 36 + 88 = 124 \) (correct)

Thus, the solution is:
- There are **18 parrots** and **22 turtles** in the zoo.