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
x, the number of visits Liam can make to earn his first free movie ticket.

1 answer

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

50 + 12.5x ≥ 160

where x is the number of visits.

To solve the inequality, we can start by subtracting 50 from both sides:

12.5x ≥ 160 - 50

Simplifying,

12.5x ≥ 110

To isolate x, we divide both sides by 12.5:

x ≥ 110 / 12.5

x ≥ 8.8

Since Liam cannot make a fraction of a visit, we round up to the nearest whole number. Therefore, Liam needs to make at least 9 visits to earn his first free movie ticket.