Question

ethan has a points card for a movie theater.

• he receives 55 rewards points just for signing up.
• he earns 12.5 points for each visit to the movie theater.
• he needs at least 150 points for a free movie ticket.

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

answer attempt 1 out of 3

inequality:

x

Explanation:

Step1: Define total points

Total points = Sign - up points + Points per visit × Number of visits. So total points is $55 + 12.5x$.

Step2: Set up inequality

He needs at least 150 points, so $55 + 12.5x \geq 150$.

Step3: Solve for x

Subtract 55 from both sides: $12.5x \geq 150 - 55 = 95$.
Divide both sides by 12.5: $x \geq \frac{95}{12.5} = 7.6$. Since the number of visits must be a whole number, $x \geq 8$.

Answer:

Inequality: $55 + 12.5x \geq 150$; Solution: $x \geq 8$ (where $x$ is the number of visits)