# 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 theatre. – 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 firs free movie ticket?

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## Question:

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 theatre. – 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 firs free movie ticket? A 3.5x+15≥553.5x+15\ge553.5x+15≥55
B 3.5+15x≥553.5+15x\ge553.5+15x≥55
C 3.5+15x ≤ 553.5+15x\ \le\ 553.5+15x ≤ 55
D 3.5x+15 ≤ 553.5x+15\ \le\ 553.5x+15 ≤ 55

Option A. 3.5x + 15 ≥ 55

Step-by-step explanation:

Points Rosh received for becoming a member = 15

Points Rosh received for visiting the moving theater = 3.5

Total points needed for a free movie ticket = 55

For each visit he receives 3.5 points, so for x visits he will receive 3.5x points.

Total points = Points received on becoming a member + Points received on x visits

So,

Total Points = 15 + 3.5x

These points must be at least 55 for a free movie ticket. At least means equal to or greater than. So the total points must be equal to or greater than 55 in order to earn a free movie ticket. This can be expressed as:

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3.5x + 15 ≥ 55

So, option A gives the correct answer

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