The toll to a bridge is $3.00. A three-month pass costs $7.50 and reduces the toll to $0.50. A six-month pass costs $30 and permits crossing the bridge for no additional fee. How many crossings per three-month period does it take for the three month pass to be the best deal?

The answer is: more than 3 and less than 15 crossings per 3 month period.

I don't understand how to produce that answer. I set up a compound inequality to solve:

7.5 + .5x < 3x and 7.5 + .5x < 30

x > 3 and x < 45.

This looks like you would need more than 3 and less than 45 crossings to make the three month pass the better deal. Where is my confusion?