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 Salem 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 $\$100$ from past fundraisers. The wrestling team has raised $\$16$ in the past, and they are making $\$5$ 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 Salem 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

\$100

from past fundraisers. The wrestling team has raised

\$16

in the past, and they are making

\$5

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 Equations: Let's set up the equations for each team's total earnings. For the volleyball team, they earn $\$2$ per car plus a $\$100$ bonus from past fundraisers. For the wrestling team, they earn $\$5$ per car plus a $\$16$ bonus from past earnings. We need to find when their earnings are equal.
Define Variables: Define variables: Let $x$ be the number of cars washed. Let $V$ be the total earnings of the volleyball team and $W$ be the total earnings of the wrestling team.
Write Equations: Write the equations based on the problem description: $\newline$ $V = 2x + 100$ $\newline$ $W = 5x + 16$ $\newline$ We need to find $x$ such that $V = W$ .
Solve for x: Set the equations equal to each other to solve for $x$ : $\newline$ $2x + 100 = 5x + 16$ $\newline$ Subtract $2x$ from both sides: $\newline$ $100 = 3x + 16$ $\newline$ Subtract $16$ from both sides: $\newline$ $84 = 3x$ $\newline$ Divide both sides by $3$ : $\newline$ $x = 28$
Substitute x: Substitute $x = 28$ back into either original equation to find the total earnings for each team. Using the volleyball team's equation: $\newline$ $V = 2(28) + 100$ $\newline$ $V = 56 + 100$ $\newline$ $V = 156$