SOLUTION: Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $4.50 each. If their total income fo

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $4.50 each. If their total income fo      Log On


   

Question 660494: Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $4.50 each. If their total income for 20 tickets was $60.00, how many did Ron sell?
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
x = ron's # of tickets
y = kathy's # of tickets
x + y = 20 : rearrange as x = 20 - y
2x + 4.5y = 60
Substitute the first into the second equation
2(20-y) + 4.5y = 60
Distribute the 2
40 - 2y + 4.5y = 60
Combine like terms
40 + 2.5y = 60
40 - 40 + 2.5y = 60 - 40
2.5y = 20
2.5y/2.5 = 20 / 2.5
y = 8 tickets that Kathy sold
so,
x = 20 - 8 = 12 tickets that Ron sold
Proof
2(12) + 4.5(8) = 24 + 36 = 60