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.
Step-by-step 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
