Liam has a points card for a movie theater.
He receives 50 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 160 points for a free movie ticket.
Write and solve an inequality which can be used to determine
x, the number of visits Liam can make to earn his first free movie ticket.
The inequality that can be used to determine the number of visits Liam can make to earn his first free movie ticket is:
50 + 12.5x ≥ 160
where x is the number of visits.
To solve the inequality, we can start by subtracting 50 from both sides:
12.5x ≥ 160 - 50
Simplifying,
12.5x ≥ 110
To isolate x, we divide both sides by 12.5:
x ≥ 110 / 12.5
x ≥ 8.8
Since Liam cannot make a fraction of a visit, we round up to the nearest whole number. Therefore, Liam needs to make at least 9 visits to earn his first free movie ticket.
To determine the number of visits Liam can make to earn his first free movie ticket, we can use the following inequality:
50 + 12.5x ≥ 160
Explanation:
- 50 represents the initial points Liam receives just for signing up for the points card.
- 12.5x represents the points he earns for each visit to the movie theater, where x is the number of visits.
- 160 represents the minimum number of points required to earn a free movie ticket.
To solve the inequality, we can start by subtracting 50 from both sides:
12.5x ≥ 160 - 50
This simplifies to:
12.5x ≥ 110
Finally, we can divide both sides of the inequality by 12.5:
x ≥ 110 / 12.5
Therefore, Liam needs to make at least 9 visits to the movie theater in order to earn his first free movie ticket.