Question

Liam has a points card for a movie theater.

• He receives 50 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 160 points for a free movie ticket.
Write and solve an inequality which can be used to determine , the number of visits
Liam can make to earn his first free movie ticket.

Answer 1

9 visits

Explanation:

12.5 x 9 = 112.5

112.5 + 50 = 162.5

Answer 2

x >= 9.

Explanation:

To earn a free movie ticket, Liam needs at least 160 points. He already has 50 points from signing up, so he needs 160 - 50 = <<160-50=110>>110 more points.

Each visit to the movie theater earns Liam 12.5 points, so the inequality representing the number of visits he needs to make is:

12.5 * x >= 110

To solve this inequality, we need to divide both sides by 12.5:

12.5 * x / 12.5 >= 110 / 12.5

This simplifies to:

x >= 8.8

Thus, Liam needs to make at least 9 visits to the movie theater to earn his first free movie ticket.

Therefore, the solution to the inequality is x >= 9.