Question

Trisha and Byron are washing and vacuuming cars to raise money for a class trip. Trisha raised $38 washington 5 cars and vacuuming 4 cars. Byron raises $28 by washing 4 cars and vacuuming 2 cars. Find the amount they charged to wash a car and vacuum a car.

Answer 1

They charged $6 for washing and $2 for vacuuming the car.

Explanation:

Let the charge of washing a car be 'x'.

And also let the charge of vacuuming a car be 'y'.

Now according to question, Trisha raised $38 washing 5 cars and vacuuming 4 cars.

So framing the above sentence in equation form, we get;

`5x+4y=38\ \ \ \ \ equation\ 1`

Again according to question, Byron raises $28 by washing 4 cars and vacuuming 2 cars.

So framing the above sentence in equation form, we get;

`4x+2y=28\ \ \ \ \ equation\2`

Now multiplying equation 2 by '2', we get;

`2(4x+2y)=28*2\\\\8x+4y=56\ \ \ \ equation\ 3`

Now we subtract equation 1 from equation 3 and get;

`(8x+4y)-(5x+4y)=56-38\\\\8x+4y-5x-4y=18\\\\3x=18\\\\x=(18)/(3)=6`

Now substituting the value of 'x' in equation 1, we get;

`5x+4y=38\\\\5*6+4y=38\\\\30+4y=38\\\\4y=38-30=8\\\\y=(8)/(4)=2`

Hence They charged $6 for washing and $2 for vacuuming the car.