Alonso has a points card for a movie theater.
He receives 40 reward points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 185 points for a free movie ticket.
Write and solve an inequality which can be used to determine x, the number of visits Alonso can make to earn his first free movie ticket.
The inequality to represent the situation is:
40 + 12.5x ≥ 185
Simplifying the inequality:
12.5x ≥ 185 - 40
12.5x ≥ 145
Finally, solving for x:
x ≥ 145/12.5
x ≥ 11.6
Therefore, Alonso needs to make at least 12 visits to the movie theater to earn his first free movie ticket.
Let's break down the information given and solve the inequality step-by-step:
Given:
Alonso receives 40 reward points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 185 points for a free movie ticket.
Let x be the number of visits to the movie theater.
We can write the inequality as follows:
40 + 12.5x ≥ 185
Now, let's solve the inequality step-by-step:
1. Subtract 40 from both sides of the inequality:
12.5x ≥ 185 - 40
12.5x ≥ 145
2. Divide both sides of the inequality by 12.5:
x ≥ 145 / 12.5
x ≥ 11.6
Since the number of visits (x) must be a whole number, Alonso can make a minimum of 12 visits to earn his first free movie ticket.