Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. 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? After washing _____ cars, both teams will have raised a total of $_____.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  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?   After washing _____ cars, both teams will have raised a total of $_____.

Bytelearn · Accepted Answer

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 $.

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