Question

HELP PLS!!!!!!!

Houa has a points card for a movie theater.
She receives 20 rewards points for just signing up.
She earns 7.5 points for each visit to the movie theater.
She needs at least 115 points for a free movie ticket.

Which inequality can be used to determine v, the minimum number of visits Houa needs to earn her first free movie ticket?

A. 20 + 7.5v ≤ 115
B. 7.5 (20 + v) ≤ 115
C. 20 + 7.5v ≥ 115
D. 7.5 (20 + v) ≥ 115

Answer 1

C. 20 + 7.5v ≥ 115

Explanation:

Reading the last sentence, our inequality will be _ ≥ 115 since Houa needs a minimum of 115 points. There will be no maximum.
20 is already added to one side of our inequality.

20 ≥ 115

However, she also earns 7.5 points for every movie theater visit. The number of times she visits the movie theater can be set to the variable v. Therefore, we need to multiply the number of times she sees the movie theater by 7.5, resulting in the term 7.5v. This term needs to be added to the total number of points. Therefore, our answer is:

20 + 7.5v ≥ 115

Answer 2

C. 20 + 7.5v ≥ 115

Explanation:

Given information:

• Sign-up reward = 20 points
• Reward per visit = 7.5 points
• Minimum number of points needed for a free ticket = 115

Definition of the variable:

• Let v be the number of visits.

To earn her first free movie ticket, the sum of the sign-up reward points and the reward points per visit needs to be at least 115 points.

⇒ 20 + 7.5v ≥ 115

Extension

To find the minimum number of visits Houa needs to earn her first free movie ticket, solve the inequality for v and round up to the nearest whole number:

⇒ 20 + 7.5v ≥ 115

⇒ 20 + 7.5v - 20 ≥ 115 - 20

⇒ 7.5v ≥ 95

⇒ 7.5v ÷ 7.5 ≥ 95 ÷ 7.5

⇒ v ≥ 12.666...

Therefore, Houa needs to visit the movie theater at least 13 times in order for her to earn enough points for her first free movie ticket.