Question

Choose the system of equations that models the situation below.



A community theater sold a total of 400 full-price tickets for adults and children. The price was $8.00 per adult ticket and $5.00 per children’s ticket. If the total revenue was $2,750, how many adult tickets, a, and how many children’s tickets, c, were sold?

Answer 1

Let a = number of adult tickets and c = number of children’s tickets.

System:
a + c = 400
8a + 5c = 2750

Solve: c = 400 − a, substitute into revenue:
8a + 5(400 − a) = 2750 → 8a + 2000 − 5a = 2750 → 3a = 750 → a = 250.
Then c = 400 − 250 = 150.

So 250 adult tickets and 150 children’s tickets were sold.