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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 Newton High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $5\$5 per car. In addition, they have already brought in $10\$10 from past fundraisers. The wrestling team has raised $101\$101 in the past, and they are making $4\$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?\newlineAfter washing ____\_\_\_\_ cars, both teams will have raised a total of $____\$\_\_\_\_.

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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 Newton High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $5\$5 per car. In addition, they have already brought in $10\$10 from past fundraisers. The wrestling team has raised $101\$101 in the past, and they are making $4\$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?\newlineAfter washing ____\_\_\_\_ cars, both teams will have raised a total of $____\$\_\_\_\_.
  1. Define Variables: Let's define the variables:\newlineLet xx be the number of cars washed.\newlineLet VV be the total amount raised by the volleyball team.\newlineLet WW be the total amount raised by the wrestling team.
  2. Volleyball Team Equation: We can write the equation for the volleyball team's total amount raised as:\newlineV=5x+10V = 5x + 10\newlineThis is because they get $5\$5 per car and have already raised $10\$10.
  3. Wrestling Team Equation: Similarly, we can write the equation for the wrestling team's total amount raised as:\newlineW=4x+101W = 4x + 101\newlineThis is because they get $4\$4 per car and have already raised $101\$101.
  4. 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:\newline5x+10=4x+1015x + 10 = 4x + 101
  5. Solve for x: Now, we solve for x using substitution or elimination. In this case, we'll subtract 4x4x from both sides to isolate x: 5x−4x+10=4x−4x+1015x - 4x + 10 = 4x - 4x + 101 x+10=101x + 10 = 101
  6. Substitute xx into VV: Next, we subtract 1010 from both sides to solve for xx:x+10−10=101−10x + 10 - 10 = 101 - 10x=91x = 91
  7. Check WW equals 465465: Now that we have the number of cars, xx, we can find the total amount raised by substituting xx back into either VV or WW. We'll use VV:
    V=5x+10V = 5x + 10
    V=5(91)+10V = 5(91) + 10
    V=455+10V = 455 + 10
    46546500
  8. Check WW equals 465465: Now that we have the number of cars, xx, we can find the total amount raised by substituting xx back into either VV or WW. We'll use VV:
    V=5x+10V = 5x + 10
    V=5(91)+10V = 5(91) + 10
    V=455+10V = 455 + 10
    46546500We should check that WW also equals 465465 when 46546533 to ensure our solution is correct:
    46546544
    46546555
    46546566
    46546577

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