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

1 answer

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.