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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.The volleyball team and the wrestling team at Westminster High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets per car. In addition, they have already brought in from past fundraisers. The wrestling team has raised in the past, and they are making 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?Each team will have raised a total of after washing cars.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.The volleyball team and the wrestling team at Westminster High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets per car. In addition, they have already brought in from past fundraisers. The wrestling team has raised in the past, and they are making 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?Each team will have raised a total of after washing cars.
- Define Variables: Let's define the variables.Let be the number of cars washed.The volleyball team earns per car plus an initial , so their total earnings can be represented as .The wrestling team earns per car plus an initial , so their total earnings can be represented as .We want to find the value of for which both teams have raised the same total amount.
- Write Equations: Write the system of equations.The volleyball team's earnings: The wrestling team's earnings: Since both teams will have raised the same amount, we can set these two expressions equal to each other to form the equation:
- Solve Equation: Solve the equation for . Subtract from both sides: Subtract from both sides: So, the number of cars washed for the teams to have raised the same amount is .
- Calculate Total Amount: Calculate the total amount raised by each team.Now that we know , we can substitute this value into either team's earnings equation to find the total amount raised.Using the volleyball team's earnings equation:So, each team will have raised a total of after washing cars.
