Question

A movie theater charges different prices for children and adults. On Friday, 10 adults and 25 children went to the movie and it cost $670. On Sunday 5 adults and 10 children went and it cost $290.

Let c = the price of a child’s ticket

Let a = the price of an adult ticket

What is the cost of each adult ticket?

Answer 1

Let a = adult price, c = child price.

From the problem:
10a + 25c = 670
5a + 10c = 290

Multiply the second equation by 2:
10a + 20c = 580

Subtract from the first:
(10a+25c) - (10a+20c) = 670 - 580
5c = 90 → c = 18

Substitute into 5a + 10c = 290:
5a + 180 = 290 → 5a = 110 → a = 22

Each adult ticket costs $22.