help me pleasee im stuck

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

Answer 1

Let y = #points earned and x = number of visits made.

Since he receives 12.5 points for each visit the expression 12.5x represents the number of points earned for x visits.

That means y = 12,5x + 50 (the 50 points added here represent the reward points for signing up). In order to get a free movie ticket, the total points earned must be at least 160, i.e. 160 points OR more.

The inequality that models this situation:

12.5x + 50 ≥ 160

12.5 x ≥ 110

x ≥ 110/12.5

x ≥ 8.8

Since he cannot make 0.8 visits, he must make a 9th visit in order to get the free movie ticket.