Cooper has a points card for a movie theater.

Question

He receives 70 rewards points just for signing up.
He earns 8.5 points for each visit to the movie theater.
He needs at least 260 points for a free movie ticket.

Which inequality can be used to determine vv, the minimum number of visits Cooper needs to earn his first free movie ticket?
Answer
Multiple Choice Answers
260, is greater than or equal to, 70, v, plus, 8, point, 5260≥70v+8.5
70, plus, 8, point, 5, v, is less than or equal to, 26070+8.5v≤260
70, plus, 8, point, 5, v, is greater than or equal to, 26070+8.5v≥260
260, is less than or equal to, 70, v, plus, 8, point, 5260≤70v+8.5

Answer 1

To determine the inequality for the minimum number of visits $v$ that Cooper needs to earn his first free movie ticket, we can analyze the points he earns.

Cooper starts with 70 points and earns 8.5 points for each visit to the theater. Therefore, after $v$ visits, his total points can be expressed as:

$$\text{Total Points}=70+8.5v$$

He needs at least 260 points to earn a free movie ticket. This leads to the following inequality:

$$70+8.5v\ge 260$$

Now, let's match this with the provided options. The correct option can be seen as:

70 + 8.5v ≥ 260

So the answer is:

70 + 8.5v ≥ 260