Question

At Fridays football game, 1,294 tickets were sold for a total amount of $8,816.00. if each student ticket cost $5.00, and each adult ticket costs $8.00 , how many student tickets were purchased?

Answer 1

512 student tickets were purchased.

Explanation:

Represenation of the unknowns: Let s be the number of student tickets and a the number of adult tickets. Then s + a = 1294.

The dollar amounts are thus ($5/ticket)s + (8/ticket)a = $8816.

Goal: Find s; to do this, eliminate a.

Since s + a = 1294, a = 1294 - s

Then: 5s + 8(1294 - s) = 8816, or

5s - 8s + 8(1294) = 8816, or

-3s + 10352 = 8816

Isolating the 3s term, we get

-3s - 1536 = 0, or

3s = 1536, which yields s = 512

512 student tickets were purchased.