Aiden has a points card for a movie theater.
He receives 75 rewards points just for signing up.
He earns 2.5 points for each visit to the movie theater.
He needs at least 90 points for a free movie ticket.
After signing up, Aiden has 75 points.
He needs at least 90 points for a free movie ticket.
That means he needs 15 more points to reach the minimum for a free movie ticket.
He earns 2.5 points for each visit to the movie theater.
So, he needs to go to the movie theater a total of 6 times to earn enough points for a free movie ticket.
write an inequality representing vv, the number of visits he needs to make in order to get a free movie ticket.
Let \( vv \) represent the number of visits Aiden needs to make in order to get a free movie ticket.
The total points Aiden earns from his visits can be represented as \( 2.5 \times vv \).
Since he already has 75 points (including the sign-up bonus), the total points he will have after \( vv \) visits is given by \( 75 + 2.5vv \).
In order to get a free movie ticket, he needs at least 90 points.
Therefore, we can write the inequality as:
\[ 75 + 2.5vv \geq 90 \]