SOLUTION: Tickets to a concert that were purchased in advance cost $4.50 each, and tickets purchased at the box office on the day of the concert cost $8.00 each. The total amount of money co

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Question 1143681: Tickets to a concert that were purchased in advance cost $4.50 each, and tickets purchased at the box office on the day of the concert cost $8.00 each. The total amount of money collected in ticket sales was the same as if every ticket purchased had cost $6.00. If 180 tickets were purchased in advance, what was the total number of tickets purchased at the box office?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
x, in advance
y, at box office

system%284.5x%2B8y=6%28x%2By%29%2Cx=180%29
Question asks for y.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

            This problem is for one single unknown, actually. 


Let x  be the number of tickets purchased at the box office (the unknown value under the question).


Then you have this equation for total money  (the "revenue" equation)


    4.50*180 + 8x = 6*(180 + x).      (1)


Should I explain it in more details ?  --  I think no, since it is quite OBVIOUS: the equation is self-explanatory.


Now simplify the equation and solve it for x :


    810 + 8x = 1080 + 6x

    8x - 6x  = 1080 - 810

    2x       = 270

     x       = 270/2 = 135.


ANSWER.  135 tickets were purchased at the box office.


CHECK.   Left side of the equation (1) is  4.50*180 + 8*135 = 1890 dollars.

         Right side of the equation (1) is  6*(180 + 135) = 1890 dollars.

         Both sides of the equation (1) are equal.

         It means that the solution and the answer are CORRECT (!)

Solved.