Question

6 josh has a rewards card for a movie theater. • he receives 15 points for becoming a rewards card holder. • he earns 3.5 points for each visit to the movie theater. • he needs at least 55 points to earn a free movie ticket. which inequality can josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket? a ( 55 geq 3.5x + 15 ) b ( 55 geq 15x + 3.5 ) c ( 55 leq 3.5x + 15 ) d ( 55 leq 15x + 3.5 )

Explanation:

Step1: Analyze total points

Josh gets 15 points initially and 3.5 points per visit (\( x \) visits). So total points = \( 3.5x + 15 \).

Step2: Relate to free ticket

He needs at least 55 points, meaning total points (\( 3.5x + 15 \)) must be greater than or equal to 55. So \( 55 \leq 3.5x + 15 \).

Answer:

C. \( 55 \leq 3.5x + 15 \)