Ethan has a points card for a movie theater.He receives 55 rewards points just for signing up.He earns 12.5 points for each visit to the movie theater.He needs at least 150 points for a free movie ticket.Write and solve an inequality which can be used to determine xx, the number of visits Ethan can make to earn his first free movie ticket.Answer Attempt 1 out of 3 Inequality: xx
12.5x + 55 ≥ 150
X equals what?
To find the value of x, we solve the inequality:
12.5x + 55 ≥ 150
Subtract 55 from both sides:
12.5x ≥ 150 - 55
12.5x ≥ 95
Divide both sides by 12.5:
x ≥ 95/12.5
x ≥ 7.6
Therefore, Ethan must make at least 8 visits to the movie theater to earn his first free movie ticket.
To determine the number of visits Ethan can make to earn his first free movie ticket, we can use an inequality.
Let's define xx as the number of visits Ethan makes to the movie theater.
We know that Ethan receives 55 rewards points just for signing up and earns 12.5 points for each visit. So his total number of points earned is given by:
Total Points = 55 + 12.5x
He needs at least 150 points for a free movie ticket. Therefore, we can set up the inequality:
Total Points ≥ 150
Substituting the expression for the total points, we get:
55 + 12.5x ≥ 150
Solving this inequality will give us the maximum number of visits (xx) Ethan can make to earn his first free movie ticket.