Question

Shandra has a points card for a movie theater.

• She receives 80 rewards points just for signing up.
• She earns 12.5 points for each visit to the movie theater.
• She needs at least 185 points for a free movie ticket.
Write and solve an inequality which can be used to determine v, the number of visits Shandra can make to earn her first free movie ticket.

Answer 1

To earn a free movie ticket, Shandra needs to make at least 9 visits to the movie theater, based on the rewards points system provided.

Step-by-step explanation:

To determine the number of visits v that Shandra can make to the movie theater to earn her first free movie ticket, we need to set up an inequality using the information given:

• Shandra starts with 80 rewards points.
• She earns 12.5 points for each visit to the theater.
• She needs at least 185 points for a free ticket.

The inequality to find the number of visits v is:

80 + 12.5v ≥ 185

To solve this inequality:

1. Subtract 80 from both sides to get: 12.5v ≥ 105
2. Divide both sides by 12.5 to isolate v: v ≥ 8.4

Since Shandra cannot make a fraction of a visit, we round up to the nearest whole number. Therefore, Shandra needs to make at least 9 visits to earn a free movie ticket.