"At a school sponsored car wash, the fees charged were: $5 per car, $8 per truck, $10 per van. Twice as many cars were washed as pickup trucks. The amount collected for washing cars and pickup trucks was $360. A total of $410 was collected. Let x represent cars, y trucks, z vans, write 3 equations, and find the number of each car washed"

Question

"At a school sponsored car wash, the fees charged were: $5 per car, $8 per truck, $10 per van. Twice as many cars were washed as pickup trucks. The amount collected for washing cars and pickup trucks was $360. A total of $410 was collected. Let x represent cars, y trucks, z vans, write 3 equations, and find the number of each car washed"

Answer 1

C=2T

360=5C+8T
410=5C+8T+10V

check my thinking.

Answer 2

here is a hint,

if trucks = x then cars = 2x

then x + 2x = $360

see if you can get the rest now.
just write what they told you in equation for.

hope that helps

Answer 3

sorry, i made a mistake

8(x) + 5(2x) = 360

8 per truck, 5 per car

Answer 4

To solve this problem, we need to set up a system of equations based on the given information.

Let's define the variables:
- Let x represent the number of cars washed.
- Let y represent the number of pickup trucks washed.
- Let z represent the number of vans washed.

Based on the information given, we can derive the following equations:

1. "Twice as many cars were washed as pickup trucks."
This can be written as: x = 2y

2. "The fees collected for washing cars and pickup trucks was $360."
The fee for washing a car is $5, and the fee for washing a truck is $8. So, the equation is:
5x + 8y = 360

3. "A total of $410 was collected."
The total amount collected is the sum of the fees for cars, trucks, and vans. So, the equation is:
5x + 8y + 10z = 410

Now, we have a system of three equations with three variables. We can solve this system to find the values of x, y, and z.

To do that, we can either solve the system algebraically or use a graphing calculator. Let's solve it algebraically using substitution.

Using the equation x = 2y, we can substitute x in the other two equations:

Equation 2: 5x + 8y = 360
Substitute x with 2y:
5(2y) + 8y = 360
10y + 8y = 360
18y = 360
y = 20

Now that we have the value of y, we can substitute it back into the equations to find the values of x and z:

From equation 1: x = 2y
x = 2(20)
x = 40

From equation 3: 5x + 8y + 10z = 410
Substitute x = 40 and y = 20:
5(40) + 8(20) + 10z = 410
200 + 160 + 10z = 410
360 + 10z = 410
10z = 410 - 360
10z = 50
z = 5

Therefore, the number of cars washed (x) is 40, the number of pickup trucks washed (y) is 20, and the number of vans washed (z) is 5.