Question

Peter hired a cleaning company to clean his house. The cleaning company charges a fixed fee of $15 plus $17 per hour to clean a house.

a) Write an equation that can be used to determine, c, the total amount in dollars that the cleaning company charges to clean a house in h hours.

b) The cleaning company charged a total of $83 to clean Peter's house. How many hours did it take to clean Peter's house?

c) A second cleaning company charges $20 per hour to clean a house. The second company does not
charge a fixed fee in addition to their hourly rate. For what number of hours is the total amount charged for cleaning a house the same for both companies? Show or explain how you got your answer.

(i need help with c.)

Answer 1

5 (for c only)

Explanation:

for c:

1st cleaning company:
`y=17x+15`

2nd cleaning company:
`y=20x`

set up as a system of equations. for them to cancle out make the y of one equation negative. I'll be making the second one negative ( it doesn't matter though)

it will look like:

`y=17x+15`

`-y=-20x`

make the two equations on top of eachother and line the terms up. Then combine them. The variable "y" will cancle out and you'll be left with

`0=-3x+15`

then you will add 3x to both sides to get
`3x=15` then divide both sides by 3 to get
`x=5`

if you plug in 5 for x into both of the original equations you will see that they will both make $100 in five hours. So you answer is 5