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

The amount they charged to wash a car is $6 and vacuum a car is $2.

Explanation:

Given:

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.

Now, to find the amount they charged to wash a car and vacuum a car.

Let the amount charged for washing a car be
`x.`

And the amount charged for vacuuming a car be
`y.`

So, the total amount Trisha raised:

`5x+4y=38.`.......(1)

And, the total amount Byron raised:

`4x+2y=28.`

Now, to get the amount they charged to wash a car and vacuum a car we use elimination method:

`5x+4y=38\\4x+2y=28......* 2`

`5x+4y=38\\8x+4y=56`

`-3x=-18`

`3x=18`

Dividing both sides by 3 we get:

`x=6.`

Amount charged to wash a car = $6.

Now, putting the value of
`x` in equation (1) we get:

`5(6)+4y=38.`

`5* 6+4y=38`

`30+4y=38.`

Subtracting both sides by 30 we get:

`4y=8.`

Dividing both sides by 4 we get:

`y=2.`

Amount charged to vacuum a car = $2.

Therefore, the amount they charged to wash a car is $6 and vacuum a car is $2.