To make a profit, Jennifer needs to earn more money from selling glasses of lemonade than she spent on supplies. Let's first calculate how much it costs to make one glass of lemonade:
Cost per glass = Total cost / Number of glasses
Cost per glass = $10.25 / x (where x is the number of glasses)
To make a profit, Jennifer needs to sell each glass for more than the cost per glass. If she sells each glass for $0.45, then her revenue for x glasses would be:
Revenue = Price per glass x Number of glasses
Revenue = $0.45 x
For Jennifer to make a profit, her revenue must be greater than her cost:
Revenue > Cost
$0.45 x > $10.25 / x
Multiplying both sides by x, we get:
$0.45 x^2 > $10.25
Dividing both sides by $0.45, we get:
x^2 > 22.78
Taking the square root of both sides, we get:
x > 4.77
Since Jennifer cannot sell a fraction of a glass, the smallest number of glasses she needs to sell to make a profit is 5. Therefore, the answer is At least 5 glasses.