32. A student is selling homemade lemonade. To make the lemonade, she must buy lemons for $0.75 each. She sells each cup of lemonade for $0.50. Which of the following equations describes the overall profit, P, that the student would make by selling lemonade if x represents the number of lemons she buys and y represents the number of cups she sells?
Answer: B
P = 0.50y - 0.75x
The overall profit, P, is calculated by taking the revenue from selling lemonade and subtracting the cost of lemons. Since each cup of lemonade sells for $0.50 and each lemon costs $0.75, the equation that accurately represents this relationship is P = 0.50y - 0.75x.
A) P = 0.50x - 0.75y
This option incorrectly assigns the number of lemons (x) to the revenue part of the equation, suggesting that the profit is derived from selling lemons instead of cups of lemonade. Therefore, this equation does not correctly represent the profit calculation.
B) P = 0.50y - 0.75x
This equation correctly represents the profit by taking the total revenue from selling y cups of lemonade at $0.50 each and subtracting the total cost of purchasing x lemons at $0.75 each. This aligns perfectly with how profit is calculated, making it the correct choice.
C) P = 0.75y - 0.50x
This option reverses the roles of cost and revenue. It incorrectly states that the revenue comes from selling cups at $0.75 and costs lemons at $0.50, which is not accurate based on the given information. Thus, it does not represent the profit correctly.
D) P = 0.75x - 0.50y
This choice incorrectly suggests that the profit is derived from the cost of lemons, multiplied by the number of lemons purchased, minus the revenue from selling lemonade. This misrepresentation of profit calculation makes it an incorrect equation for the scenario presented.
Conclusion
The correct equation for calculating the overall profit from selling lemonade is P = 0.50y - 0.75x, as it accurately reflects the revenue generated from each cup sold and the total cost of lemons. The other options fail to correctly represent the relationship between costs and revenues, leading to incorrect formulations of profit.