Final answer:
A student can attend up to 64 games at nine dollars each before exceeding the cost of a $580 season ticket.
Step-by-step explanation:
The student is inquiring about at most how many basketball games they can attend for nine dollars each before they spend more than the cost of a season ticket, which is $580. To solve this, we simply need to find the largest number of games that can be attended without the total cost exceeding $580. By dividing the cost of a season ticket by the cost per game, we get:
$580 ÷ $9/game = 64.44 games
Since you can't attend a fraction of a game, we round down to the nearest whole number, which is 64. Thus, you could attend up to 64 games at nine dollars each before spending more than the cost of a season ticket.