Problem Solving

For a recent play performance, the ticket prices were $25 per adult and $15 per child. A
total of 500 tickets were sold for the performance. How many of the tickets sold were for
adults?
(1) Revenue from ticket sales for this performance totaled $10,500.
(2) The average (arithmetic mean) price per ticket sold was $21.

hjafferi wrote:For a recent play performance, the ticket prices were $25 per adult and $15 per child. A
total of 500 tickets were sold for the performance. How many of the tickets sold were for
adults?
(1) Revenue from ticket sales for this performance totaled $10,500.
(2) The average (arithmetic mean) price per ticket sold was $21.

Let A = the number of adult tickets and C = the number of children's tickets.
Since 500 tickets are sold, we get:
A + C = 500.
Total revenue = 25A + 15C.

Statement 1: Revenue from ticket sales for this performance totaled $10,500.
Thus:
25A + 15C = 10,500.
Since we have two variables and two distinct linear equations (A+C = 500 and 25A + 15C = 10,500), we can solve for each variable.
SUFFICIENT.

Statement 2: The average (arithmetic mean) price per ticket sold was $21.
Thus:
Total revenue = (number of tickets)(average price) = 500*21 = 10,500.
Same information as that given in statement 1.
SUFFICIENT.

The correct answer is D.