Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ The volleyball team and the wrestling team at Newport High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $\$1$ per car. In addition, they have already brought in $\$86$ from past fundraisers. The wrestling team has raised $\$14$ in the past, and they are making $\$3$ 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? $\newline$ Each team will have raised a total of $\$$ _ after washing _ cars.

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Solve a system of equations using substitution: word problems

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

\newline

The volleyball team and the wrestling team at Newport High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets

\$1

per car. In addition, they have already brought in

\$86

from past fundraisers. The wrestling team has raised

\$14

in the past, and they are making

\$3

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?

\newline

Each team will have raised a total of

\$

_____ after washing _____ cars.

Set up team equations: Let's set up the equations for each team's total earnings. Let $x$ be the number of cars washed. The volleyball team earns $\$1$ per car plus their previous $\$86$ , so their equation is $V = x + 86$ . The wrestling team earns $\$3$ per car plus their previous $\$14$ , so their equation is $W = 3x + 14$ .
Set equations equal: Since both teams will have raised the same total amount, we set the equations equal to each other: $x + 86 = 3x + 14$ .
Solve for x: Solve for x by subtracting $x$ from both sides and then subtracting $14$ from both sides: $86 - 14 = 3x - x$ , which simplifies to $72 = 2x$ .
Find number of cars: Divide both sides by $2$ to find $x$ : $\frac{72}{2} = x$ , so $x = 36$ . This means they need to wash $36$ cars.
Calculate total amount raised: Substitute $x = 36$ back into either team's equation to find the total amount raised. Using the volleyball team's equation: $V = 36 + 86 = 122$ .