Question

A local movie theater earned $512 on Saturday from
selling 19 adult tickets and 17 child tickets. On Sunday,
they earned $356 from selling 12 adult tickets and 14 child
tickets.
How many dollars is an adult ticket?

Answer 1

Let a = adult price, c = child price.

From Saturday: 19a + 17c = 512
From Sunday: 12a + 14c = 356

Solve the system. From the second, a = (356 − 14c)/12. Substitute in the first:
19(356 − 14c)/12 + 17c = 512
Multiply by 12: 19(356 − 14c) + 204c = 6144
19·356 = 6764? Wait check — better to keep earlier correct arithmetic:
Using earlier simpler numbers gives 3382 − 31c = 3072 → c = 10

Then a = (356 − 14·10)/12 = (356 − 140)/12 = 216/12 = 18.

So an adult ticket costs $18.