Question

The box office at a theater is selling tickets for a series of rock concerts. So far, they have sold 53 balcony tickets and 94 general admission floor tickets for Friday's show, for a total of $4,482 in receipts. For Saturday's show, 53 balcony tickets and 47 general admission floor tickets have been sold, equaling $3,354 in receipts. How much does each ticket cost?

Answer 1

Explanation:

Subtract 2nd equation from the first

53b+94g-53b-47g=4482-3354

47g=1128

g=24, using this value in 53b+94g=4482 gives you

53b+94(24)=4482

53b+2256=4482

53b=2226

b=43

So general admission tickets cost $24 and balcony tickets cost $43.

Answer 2

The box office sold 360 tickets to a concert at

the college. The total receipts were $4,170. General

admission tickets cost $15 and student tickets cost $10.

How many of each kind of ticket was sold?

Answer: 114 general admission tickets and 246 student tickets were sold.

Explanation:

Let x represent the number of general admission tickets that were sold.

Let y represent the number of student tickets that were sold.

The box office sold 360 tickets to a concert at the college. It means that

x + y = 360

General admission tickets cost $15 and student tickets cost $10. The total receipts were $4170. It means that

15x + 10y = 4170- - - - - - - - -1

Substituting x = 360 - y into equation 1, it becomes

15(360 - y) + 10y = 4170

5400 - 15y + 10y = 4170

- 15y + 10y = 4170 - 5400

- 5y = - 1230

y = - 1230/-5

y = 246

x = 360 - y = 360 - 246

x = 114