Eliminination Method Word Problem

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 $55. How many small dogs did Ryan walk?

Ryan walked _____ small dogs.

Answer 1

Let's ID our variables. s = small dogs, l = large dogs

Here's what we know:

s + l = 8

5s + 8l = 55

 

Since we need to use elimination, what we need to do is multiply the first equation by an amount that will get rid of a variable. I suggest -5 and get rid of the s. (-8 also works to get rid of the l if you so desire.)

 

-5s - 5l = -40

5s + 8l =  55

------------------

3l = 15

Divide both sides by 3:

l = 5

 

Now we can solve for small dogs:

s + 5 = 8

s = 3

 

Now to check our answer:

5 * 3 + 8 * 5 = 55

15 + 40 = 55

55 = 55