Question

Trisha and Byron are washing and vacuuming cars to raise money for a class trip. Trisha raised $38 by washing

5 cars and vacuuming 4 cars. Byron raised $28 by washing 4 cars and vacuuming 2 cars. Find the amount they
charged to wash a car and vacuum a car.

Answer 1

Explanation:

Let x = amount charged for washing a car

y = amount charged for vacuuming a car

Solution :

38 = 5x + 4y (1)

28 = 4x + 2y (2)

Can be solved by substitution or simply subtracting the (1) and (2) equation.

By Substitution:

38 = 5x + 4y ---> solve for x

38 - 4y = 5x (transposed 4y to the other side of the equation and it's sign changes from (+) to (-).

`(38-4y)/(5) =x`

substitute the value of x to the (2) equation.

28 = 4x + 2 y

`28=4((38-4y)/(5))+2y`

`28=(152-16y)/(5) +2y` , then multiply both side by 5 to eliminate the denominator 5.

140 = 152 - 16y + 10y (transposed 152 to the other side, change sign from (+) to (-)).

140 - 152 = -16y + 10 y

-12 = -6y (divide both side by (-6)

y = 2 or $2 (amount charged for vacuuming)

Using any of the 2 equation, we can solve for the value of x.

38 = 5x + 4 (2) (we substitute, the value of y)

38 - 8 = 5x

30/5 = x

x= 6 or $6 (amount charged for washing)