Respuesta :
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 [tex]x.[/tex]
And the amount charged for vacuuming a car be [tex]y.[/tex]
So, the total amount Trisha raised:
[tex]5x+4y=38.[/tex].......(1)
And, the total amount Byron raised:
[tex]4x+2y=28.[/tex]
Now, to get the amount they charged to wash a car and vacuum a car we use elimination method:
[tex]5x+4y=38\\4x+2y=28......\times 2[/tex]
[tex]5x+4y=38\\8x+4y=56[/tex]
[tex]-3x=-18[/tex]
[tex]3x=18[/tex]
Dividing both sides by 3 we get:
[tex]x=6.[/tex]
Amount charged to wash a car = $6.
Now, putting the value of [tex]x[/tex] in equation (1) we get:
[tex]5(6)+4y=38.[/tex]
[tex]5\times 6+4y=38[/tex]
[tex]30+4y=38.[/tex]
Subtracting both sides by 30 we get:
[tex]4y=8.[/tex]
Dividing both sides by 4 we get:
[tex]y=2.[/tex]
Amount charged to vacuum a car = $2.
Therefore, the amount they charged to wash a car is $6 and vacuum a car is $2.
