Question

A theater has orchestra tickets at $10, box- seat tickets at $7, and balcony tickets at $5. For one performance, a total of 360 tickets were sold in the total revenue was $3040. If the number of Orchestra tickets sold was that of the other two types combined, how many of each type of ticket was sold

Answer 1

The Answer is there were: 180 Orchestra Tickets; 170 Box Seat Tickets; and 10 Balcony seats.

Explanation:

10o + 7b + 5y = $3,040

o + b + y = 360

b + y = o

b = o - y

Substitute:

(b + y) + b + y = 360

2b + 2y = 360

2y = 360 - 2b

y = 180 - b

y - 180 = -b

-b = y - 180

b = 180 - y

10(b + y) + 7(b) + 5(180 - b) = 3040

10(b + (180 - b)) + 7b + 5(180 - b) = 3040

10b + 1800 - 10b + 7b + 900 - 5b = 3040

2b + 2700 = 3040

2b = 340

b = 170

y = 180 - 170 = 10

b + y = o

o = 170 + 10 = 180

Proof total tickets:

o + b + y = 360

180 + 170 + 10 = 360

Proof Amount:

10o + 7b + 5y = $3,040

10(180) + 7(170) + 5(10) =

1800 + 1190 + 50 = $3,040