SOLUTION: students are having a car wash to raise at least $200.00. they are charging $3.00 a car and $5.00 per van. if they wash three times as many cars as vans how many cars and vans do t

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: students are having a car wash to raise at least $200.00. they are charging $3.00 a car and $5.00 per van. if they wash three times as many cars as vans how many cars and vans do t      Log On

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Question 544257: students are having a car wash to raise at least $200.00. they are charging $3.00 a car and $5.00 per van. if they wash three times as many cars as vans how many cars and vans do they need to wash to reach their goal?
Answer by SwiftAlbatross(13) About Me  (Show Source):
You can put this solution on YOUR website!
This can be solved by setting up a system of equations with two equations and two variables. The variables, c and v, represent the number of cars and vans respectively. The equations are just the sum of $200 by adding $3 for every car plus $5 for every van, and the conversion of thrice as many cars to vans:
3c + 5v >= 200
c = 3v
Now you can solve because remember if you have as many equations as you do variables, you can solve for all variables. Just use the substitution method:
3(3v) + 5v >= 200
9v + 5v >= 200
14v >= 200
÷ 14 = ÷ 14
v >= 14 2/7
So v = 15, since they must've washed a whole number of vans. The number of cars is 3 times this amount or 15 * 3 = 45. Therefore they washed 45 cars and 15 vans to reach their goal. You can check your answer:
3*45 + 5*15 >= 200