Jimmy earns $1.50 for every video game he sells. When he sells one carton of 30 video games, he earns an additional $10. What is the minimum number of video games he has to sell in order to earn $450?

1.50n + 10.00*floor(n/30) = 450

n = 246.7

Check:
246 games: 246*1.50 + 10*8 = 449.00

Add $1.50 for the 247th game, and that puts him over the top.

To find the minimum number of video games Jimmy has to sell in order to earn $450, we need to set up an equation based on the given information.

Let's start by calculating the earnings from selling the carton of video games. Jimmy earns an additional $10 for selling one carton, which contains 30 video games. So, the earnings from selling one carton can be calculated as follows: 30 games * $10/carton = $300.

Now, let's calculate the earnings from selling individual video games. Jimmy earns $1.50 for every video game he sells. Let's assume he needs to sell x number of video games to earn a total of $450. Therefore, the earnings from selling individual video games can be calculated as follows: x games * $1.50/game = $450.

Now, we can set up an equation by combining the earnings from selling a carton and selling individual video games to get the total earnings: $300 + $1.50x = $450.

To find the minimum number of video games Jimmy has to sell, we need to solve this equation for x.

Subtract $300 from both sides of the equation: $1.50x = $150.

Divide both sides of the equation by $1.50 to solve for x: x = $150 / $1.50 = 100.

Therefore, Jimmy has to sell a minimum of 100 video games in order to earn $450.