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 Danville 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 $\$101$ from past fundraisers. The wrestling team has raised $\$10$ in the past, and they are making $\$2$ 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 $\$\_\_\_\_$ .

View step-by-step help

Home

Math Problems

Precalculus

Solve a system of equations using substitution: word problems

Full solution

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 Danville 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

\$101

from past fundraisers. The wrestling team has raised

\$10

in the past, and they are making

\$2

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

\$\_\_\_\_

Set up 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 $101$ from past fundraisers, so their equation is $V = x + 101$ . The wrestling team earns $2$ per car plus $10$ from past fundraisers, so their equation is $W = 2x + 10$ .
Equalize equations: Since both teams will have raised the same total amount, we set the equations equal to each other: $x + 101 = 2x + 10$ .
Solve for x: Solve for $x$ by subtracting $x$ from both sides: $101 = x + 10$ .
Isolate x: Subtract $10$ from both sides to isolate $x$ : $x = 91$ .
Find total amount raised: Plug $x = 91$ back into either original equation to find the total amount raised by each team. Using the volleyball team's equation: $V = 91 + 101 = 192$ .