Ramon rented a sprayer and a generator. On his first job, he used each piece of equipment for 6 hours at a total cost of $90. On his second job, he used the sprayer for 4 hours and the generator for 8 hours at a total cost of $100 What was the hourly cost for the sprayer?

Name Variables:

The hourly cost of the sprayer: x

Hourly cost of the generator: y


First job: 

6x+6y=90

Second job: 

4x+8y=100

__Going back to first job__

6x+6y=90

-divide by 6 on both sides to isolate the variables-

x+y=15

-We can choose to get either x or y by itself, I will choose y-
-Subtract by x on both sides-

y=15-x

__We can sub in what we got from job 1 for job 2__


4x+8(15-x)=100

-distribute-

4x+120-8x=100

-subtract by 120 on both sides-

-4x=-20

-divide by -4 to get x by itself-

x=5

_____Now we know x so we can sub into the equation for job 1 to find y____

6(5)+6y=90

-distribute-

30+6y=90

-subtract 30 from both sides-

6y=60

-divide by 6 to get y by itself-

y=10
___________________________________________________________
Final Answer:

Hourly cost of sprayer=5$

Hourly cost of generator=10$