The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 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. What will that total be? How many cars will that take?
Set up the earnings equation for the volleyball team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 4w + 81
Set up the earnings equation for the wrestling team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 2w + 85
If the raised the same amount in total, set both earnings equations equal to each other:
4w + 81 = 2w + 85
Solve for w in the equation 4w + 81 = 2w + 85
Step 1: Group variables:
We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides
4w + 81 - 2w = 2w + 85 - 2w
Step 2: Cancel 2w on the right side:
2w + 81 = 85
Step 3: Group constants:
We need to group our constants 81 and 85. To do that, we subtract 81 from both sides
2w + 81 - 81 = 85 - 81
Step 4: Cancel 81 on the left side:
2w = 4
Step 5: Divide each side of the equation by 2
2w/2 = 4/2
w = 2 <-- How many cars it will take
To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2:
E = 4(2) + 81
E = 8 + 81
E = 89 <-- Total Earnings
Set up the earnings equation for the volleyball team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 4w + 81
Set up the earnings equation for the wrestling team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 2w + 85
If the raised the same amount in total, set both earnings equations equal to each other:
4w + 81 = 2w + 85
Solve for w in the equation 4w + 81 = 2w + 85
Step 1: Group variables:
We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides
4w + 81 - 2w = 2w + 85 - 2w
Step 2: Cancel 2w on the right side:
2w + 81 = 85
Step 3: Group constants:
We need to group our constants 81 and 85. To do that, we subtract 81 from both sides
2w + 81 - 81 = 85 - 81
Step 4: Cancel 81 on the left side:
2w = 4
Step 5: Divide each side of the equation by 2
2w/2 = 4/2
w = 2 <-- How many cars it will take
To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2:
E = 4(2) + 81
E = 8 + 81
E = 89 <-- Total Earnings