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 Newton High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $\$5$ per car. In addition, they have already brought in $\$10$ from past fundraisers. The wrestling team has raised $\$101$ 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. How many cars will that take? What will that total be? $\newline$ After washing $\_\_\_\_$ cars, both teams will have raised a total of $\$\_\_\_\_$ .

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

\$5

per car. In addition, they have already brought in

\$10

from past fundraisers. The wrestling team has raised

\$101

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. How many cars will that take? What will that total be?

\newline

After washing

\_\_\_\_

cars, both teams will have raised a total of

\$\_\_\_\_

Define Variables: Let's define the variables: $\newline$ Let $x$ be the number of cars washed. $\newline$ Let $V$ be the total amount raised by the volleyball team. $\newline$ Let $W$ be the total amount raised by the wrestling team.
Volleyball Team Equation: We can write the equation for the volleyball team's total amount raised as: $\newline$ $V = 5x + 10$ $\newline$ This is because they get $\$5$ per car and have already raised $\$10$ .
Wrestling Team Equation: Similarly, we can write the equation for the wrestling team's total amount raised as: $\newline$ $W = 4x + 101$ $\newline$ This is because they get $\$4$ per car and have already raised $\$101$ .
Set Equations Equal: Since we are told that after washing a certain number of cars, each team will have raised the same amount in total, we can set the two equations equal to each other: $\newline$ $5x + 10 = 4x + 101$
Solve for x: Now, we solve for x using substitution or elimination. In this case, we'll subtract $4x$ from both sides to isolate x: $5x - 4x + 10 = 4x - 4x + 101$ $x + 10 = 101$
Substitute $x$ into $V$ : Next, we subtract $10$ from both sides to solve for $x$ : $x + 10 - 10 = 101 - 10$ $x = 91$
Check $W$ equals $465$ : Now that we have the number of cars, $x$ , we can find the total amount raised by substituting $x$ back into either $V$ or $W$ . We'll use $V$ :
$V = 5x + 10$
$V = 5(91) + 10$
$V = 455 + 10$
$465$ $0$
Check $W$ equals $465$ : Now that we have the number of cars, $x$ , we can find the total amount raised by substituting $x$ back into either $V$ or $W$ . We'll use $V$ :
$V = 5x + 10$
$V = 5(91) + 10$
$V = 455 + 10$
$465$ $0$ We should check that $W$ also equals $465$ when $465$ $3$ to ensure our solution is correct:
$465$ $4$
$465$ $5$
$465$ $6$
$465$ $7$