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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?

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carlosego

Answer: 56 large cars and 86 small cars.

Step-by-step explanation:

Let's call:

[tex]l[/tex]: the number of large cars.

[tex]s[/tex]: the number of small cars.

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

[tex]\left \{ {{l+s=142} \atop {5.50l+4.0s=652.50}} \right.[/tex]

You can use the Elimination Method:

- Multiply the first equation by -4.0

- Add both equations.

- Solve for l.

[tex]\left \{ {{-4.0l-4.0s=-568} \atop {5.50l+4.0s=652.50}} \right.\\--------\\1.5l=84.5[/tex]

[tex]l[/tex]≈[tex]56[/tex]

Substitute [tex]l=56[/tex] into one of the original equations and solve for s:

[tex]56+s=142\\s=142-56\\s=86[/tex]

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