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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineThe 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\$1 per car. In addition, they have already brought in $86\$86 from past fundraisers. The wrestling team has raised $14\$14 in the past, and they are making $3\$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?\newlineEach team will have raised a total of $\$_____ after washing _____ cars.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineThe 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\$1 per car. In addition, they have already brought in $86\$86 from past fundraisers. The wrestling team has raised $14\$14 in the past, and they are making $3\$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?\newlineEach team will have raised a total of $\$_____ after washing _____ cars.
  1. Set up team equations: Let's set up the equations for each team's total earnings. Let xx be the number of cars washed. The volleyball team earns $1\$1 per car plus their previous $86\$86, so their equation is V=x+86V = x + 86. The wrestling team earns $3\$3 per car plus their previous $14\$14, so their equation is W=3x+14W = 3x + 14.
  2. Set equations equal: Since both teams will have raised the same total amount, we set the equations equal to each other: x+86=3x+14x + 86 = 3x + 14.
  3. Solve for x: Solve for x by subtracting xx from both sides and then subtracting 1414 from both sides: 86−14=3x−x86 - 14 = 3x - x, which simplifies to 72=2x72 = 2x.
  4. Find number of cars: Divide both sides by 22 to find xx: 722=x\frac{72}{2} = x, so x=36x = 36. This means they need to wash 3636 cars.
  5. Calculate total amount raised: Substitute x=36x = 36 back into either team's equation to find the total amount raised. Using the volleyball team's equation: V=36+86=122V = 36 + 86 = 122.

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