Question

Owen has a points card for a movie theater.
He receives 30 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 115 points for a free movie ticket.

Write and solve an inequality which can be used to determine
x, the number of visits Owen can make to earn his first free movie ticket.
Answer

Answer 1

The inequality that can be used to determine the number of visits Owen can make to earn his first free movie ticket is:

30 + 12.5x ≥ 115

Where x is the number of visits Owen makes.

To solve for x:
Subtract 30 from both sides of the inequality:

12.5x ≥ 115 - 30

12.5x ≥ 85

Divide both sides of the inequality by 12.5:

x ≥ 85/12.5

x ≥ 6.8

Since the number of visits must be a whole number, Owen can make at least 7 visits to earn his first free movie ticket.