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Idil has a points card for a movie theater.
She receives 85 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 155 points for a free movie ticket.
Write and solve an inequality which can be used to determine xx, the number of visits Idil can make to earn her first free movie ticket.
Let's use the inequality to represent the situation:
85 + 12.5x ≥ 155
In this inequality, "x" represents the number of visits Idil can make to earn her first free movie ticket. The left side of the inequality represents the total number of points she has accumulated by signing up and the points earned from the visits. The right side of the inequality represents the minimum number of points required for a free movie ticket.
Now, we can solve this inequality:
85 + 12.5x ≥ 155
12.5x ≥ 155 - 85
12.5x ≥ 70
x ≥ 70 / 12.5
x ≥ 5.6
Since the number of visits cannot be a decimal, Idil would need to make at least 6 visits to the movie theater in order to earn her first free movie ticket.