Question

The high school leadership team is having a car wash. They charge $5.50 for large cars and $4.00 for small cars . They had a successful day, washed a total of 142 cars, and made $652.50. How many large cars and small cars did they wash?

Answer 1

Answer: 56 large cars and 86 small cars.

Explanation:

Let's call:

`l`: the number of large cars.

`s`: the number of small cars.

Then, you can set up the following system of equations:

`\left \{ {{l+s=142} \atop {5.50l+4.0s=652.50}} \right.`

You can use the Elimination Method:

- Multiply the first equation by -4.0

- Add both equations.

- Solve for l.

`\left \{ {{-4.0l-4.0s=-568} \atop {5.50l+4.0s=652.50}} \right.\\--------\\1.5l=84.5`

`l`≈
`56`

Substitute
`l=56` into one of the original equations and solve for s:

`56+s=142\\s=142-56\\s=86`