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

Answer:

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

Step-by-step 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:

$5x+4y=38\\4x+2y=28......\times 2$

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

$-3x=-18$

$3x=18$

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:

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

$5\times 6+4y=38$

$30+4y=38.$

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.