A concert manager counted 350 ticket receipts the day after a concert. The price for the student ticket was $12.50, and the price for the adult ticket was $16. The register confirms that $5,075 was taken in. Using this information, we can construct a system of equations to determine the number of student and adult tickets that were sold for the concert.
Let s = the number of student tickets sold and a = the number of adult tickets sold.
We know that the total number of tickets sold was 350. Therefore, s+a = 350.
12.50s = the amount of money taken in from student tickets
16a = the amount of money taken in from adult tickets
12.50 + 16a = the total amount of money taken in
We can write our system of equations as:
(1) s+a = 350
(2) 12.50s+16a = 5075
Using the system of equations above, and the substitution method for solving the system, determine the number of student and adult tickets sold. Show your work.