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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. The volleyball team and the wrestling team at Brookfield High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $2 per car. In addition, they have already brought in $92 from past fundraisers. The wrestling team has raised $16 in the past, and they are making $4 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take?

Respuesta :

Data:

Volleyball team: V

Wrestling team: W

x: number of cars

V: $2 per car. Initial $92

W: $4 per car. Initial $16

You have the next equations:

[tex]\begin{gathered} V=2x+92 \\ W=4x+16 \end{gathered}[/tex]

To find the total amount you have the next equation:

As each team have raised the same amount:

[tex]\begin{gathered} V=W \\ \\ 2x+92=4x+16 \end{gathered}[/tex]

You solve x to find the number of cars each team wash in total:

[tex]\begin{gathered} 2x-4x+92=4x-4x+16 \\ -2x+92=16 \\ \\ -2x+92-92=16-92 \\ -2x=-76 \\ \\ \frac{-2}{-2}x=\frac{-76}{-2} \\ x=38 \end{gathered}[/tex]

You use that value of x to find the final amount of each team:

[tex]\begin{gathered} V=2(38)+92=76+92=168 \\ \\ W=4(38)+12=152+12=168 \end{gathered}[/tex]Then, (the total of each team is $168) Total $336, (each team wash 38 cars) The total number of cars 76

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