Jocelyn has a points card for a movie theater.
She receives 25 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 170 points for a free movie ticket.
Write and solve an inequality which can be used to determine vv, the number of visits Jocelyn can make to earn her first free movie ticket.
Let vv be the number of visits Jocelyn can make to earn her first free movie ticket.
The total number of points she can earn from visits is 12.5 * vv.
Therefore, the inequality to represent this situation is:
25 + 12.5 * vv ≥ 170
To solve for vv, we need to isolate the variable vv.
First, subtract 25 from both sides of the inequality:
12.5 * vv ≥ 170 - 25
12.5 * vv ≥ 145
Next, divide both sides of the inequality by 12.5:
vv ≥ 145 / 12.5
vv ≥ 11.6
Since the number of visits must be a whole number, the smallest number of visits Jocelyn needs to earn her first free movie ticket is 12 visits.