Valeria has a points card for a movie theater.
She receives 35 rewards points just for signing up.
She earns 11.5 points for each visit to the movie theater.
She needs at least 55 points for a free movie ticket.
Which inequality can be used to determine vv, the minimum number of visits Valeria needs to earn her first free movie ticket?
To determine the minimum number of visits Valeria needs to earn her first free movie ticket, we can create an inequality involving the initial reward points she receives for signing up and the points she earns per visit.
Valeria starts with 35 reward points, and each visit to the movie theater earns her an additional 11.5 points. Let v represent the number of visits to the theater. She needs at least 55 points to earn a free movie ticket. Therefore, the total points that Valeria earns after v visits will be her initial 35 points plus 11.5 points per visit.
The inequality that represents this scenario is:
35 + 11.5v ≥ 55
This inequality states that the points she starts with (35) plus the points she earns per visit (11.5v) must be greater than or equal to the number required for a free movie ticket (55). Solving for v will give us the minimum number of visits Valeria needs.