Question

Ryan earns $5
for each small dog he walks and $8
for each large dog he walks. Today he walked 8
dogs and made a total of $49
. How many small dogs did Ryan walk?

Answer 1

Let the number of small dogs Ryan walked be \( x \) and the number of large dogs be \( y \).

We have the following system of equations based on the information provided:

1. The total number of dogs he walked:
\[
x + y = 8
\]

2. The total amount of money he made:
\[
5x + 8y = 49
\]

We can solve this system of equations. Starting from the first equation, we can express \( y \) in terms of \( x \):
\[
y = 8 - x
\]

Now, we can substitute this expression for \( y \) into the second equation:
\[
5x + 8(8 - x) = 49
\]

Expanding this gives:
\[
5x + 64 - 8x = 49
\]

Combining like terms, we can rewrite this as:
\[
-3x + 64 = 49
\]

Next, we can isolate \( x \):
\[
-3x = 49 - 64
\]
\[
-3x = -15
\]
\[
x = 5
\]

So, Ryan walked \( \boxed{5} \) small dogs.

To find the number of large dogs, we can substitute \( x = 5 \) back into the equation for \( y \):
\[
y = 8 - x = 8 - 5 = 3
\]

Ryan walked 3 large dogs as well. Let’s check the total earnings:
\[
5(5) + 8(3) = 25 + 24 = 49
\]

The calculations confirm that Ryan indeed earned $49, verifying that he walked \( \boxed{5} \) small dogs.