Owen has a points card for a movie theater.
He receives 30 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 115 points for a free movie ticket.
Write and solve an inequality which can be used to determine
x, the number of visits Owen can make to earn his first free movie ticket.
Answer
The inequality that can be used to determine the number of visits Owen can make to earn his first free movie ticket is:
30 + 12.5x ≥ 115
Where x is the number of visits Owen makes.
To solve for x:
Subtract 30 from both sides of the inequality:
12.5x ≥ 115 - 30
12.5x ≥ 85
Divide both sides of the inequality by 12.5:
x ≥ 85/12.5
x ≥ 6.8
Since the number of visits must be a whole number, Owen can make at least 7 visits to earn his first free movie ticket.
The inequality that can be used to determine the number of visits Owen can make to earn his first free movie ticket is:
30 + 12.5x ≥ 115
Where x represents the number of visits Owen can make.
To solve for x, we need to isolate it on one side of the inequality:
12.5x ≥ 115 - 30
12.5x ≥ 85
Now, divide both sides of the inequality by 12.5:
x ≥ 85 / 12.5
x ≥ 6.8
Since Owen cannot make a fraction of a visit, we round up to the nearest whole number:
x ≥ 7
Therefore, Owen needs to make at least 7 visits to the movie theater to earn his first free movie ticket.