Pls help me im stuck :(

Question

Jose has a points card for a movie theater.

1. He receives 50 rewards points just for signing up.
2. He earns 3.5 points for each visit to the movie theater.
3. He needs at least 85 points for a free movie ticket.

Write and solve an inequality which can be used to determine xx, the number of visits Jose can make to earn his first free movie ticket.

Answer 1

Let's call V the number of visits (better than x). He gets 3.5 points for each visit, so for V visits he gets 3.5V points. Then there's the 50 reward points just for signing up. So the expression for total points would be 3.5V + 50. He needs at least 85 points for a freebee so the inequality would be 3.5V + 50 ≥ 85. Can you solve for V? (Hint: the answer is a nice round number).

Answer 2

Answer 3

Put simply, we need to figure out when we will have enough reward points to get a free movie ticket.

Reward points EARNED ≥ Reward points needed for a free movie ticket

We start with 50 points and its a one time so we should add 50 to out total rewards points.

Then we have to add 3.5 points for every movie theatre visit, this means we multiply 3.5 by however many times we have visited which is xx

50 + 3.5x ≥ 85

This is our inequality, Note that 85 is the number of reward points we need to get a free movie ticket.

Now we must get x alone. Start by canceling out the constant term ( the term without x in it)

50 + 3.5x ≥ 85

-50 -50

We simplify to get the following

3.5x ≥ 35

Now we need to cancel out the term in front of the x, by dividing both sides by 3.5

3.5x⁄ 3.5 ≥ 35/3.5

simplify to get

x ≥ 10

so we need to visit the theatre 10 or more times before we have enough point for a free movie