Lauren opened a lemonade stand on her street. It costs her $8.00 to buy the supplies each day, and she sells lemonade for $2.50 a cup.
If she wants to make at least $175.00 in profits (sales - expenses) each day, what is the minimum number of cups of lemonade Lauren needs to sell? Input your answer as a whole number.
Let's call the number of cups she needs to sell x.
The total expenses each day are $8.00.
The total sales each day are $2.50 * x.
Lauren's profit each day is the total sales minus the total expenses, so x * $2.50 - $8.00.
We need to find x such that x * $2.50 - $8.00 >= $175.00.
Simplifying the inequality, we have x * $2.50 >= $175.00 + $8.00.
Combining like terms, we have x * $2.50 >= $183.00.
Dividing both sides by $2.50, we have x >= $183.00 / $2.50.
Simplifying the right side, we have x >= 73.2.
Since x must be a whole number, the minimum number of cups she needs to sell is 74. Answer: \boxed{74}.