Answer: the number of student tickets sold is 150
the number of adult tickets sold at the concert is 425
Step-by-step explanation:
Let x represent the number of student tickets sold at the concert.
Let y represent the number of adult tickets sold at the concert.
The concert manager counted 575 ticket receipts the day after the concert. This means that
x + y = 575
The price for a student ticket was $11.50, and the price for an adult ticket was $14.00. The register confirms that $7,675.00 was taken in. This means that
11.5x + 14y = 7675 - - - - - - - - - -1
Substituting x = 575 - y into equation 1, it becomes
11.5(575 - y) + 14y = 7675
6612.5 - 11.5y + 14y = 7675
- 11.5y + 14y = 7675 - 6612.5
2.5y = 1062.5
y = 1062.5/2.5 = 425
Substituting y = 425 into x = 575 - y, it becomes
x = 575 - 425 = 150
