Answer: 340 senior citizen tickets were sold
Step-by-step explanation:
Let x represent the number of senior tickets that were sold.
Let y represent the number of adult tickets that were sold.
The University theater sold 491 tickets for a play. This means that
x + y = 491
Tickets cost $25 per adult and $13 per senior citizen. If total receipts were $8195, it means that
13x + 25y = 8195 - - - - - -- - -- -- -1
Substituting x = 491 - y into equation 1, it becomes
13(491 - y) + 25y = 8195
6383 - 13y + 25y = 8195
- 13y + 25y = 8195 - 6383
12y = 1812
y = 1812/12
y = 151
Substituting y = 151 into x = 491 - y, it becomes
x = 491 - 151
x = 340
