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?
P = 0.50y - 0.75x
To calculate the overall profit, P, from selling lemonade, we need to consider the revenue generated from selling cups and the cost incurred from purchasing lemons. Selling each cup for $0.50 and buying each lemon for $0.75 leads to the equation where profit is calculated as the total revenue ($0.50y) minus the total cost ($0.75x).
This equation incorrectly relates the revenue to the number of lemons (x) instead of the number of cups sold (y). The revenue should come from the number of cups sold, which is represented by y, while the cost should be deducted based on the lemons bought. Therefore, this option does not accurately represent the profit calculation.
This option correctly represents the profit equation by subtracting the total cost of lemons (0.75x) from the total revenue from selling lemonade (0.50y). It effectively shows that profit is derived from the revenue obtained minus the expenses incurred, making it the correct choice.
This equation mistakenly suggests that the profit comes from a revenue of $0.75 per cup sold, which is incorrect as the selling price is $0.50 per cup. It also incorrectly places the selling price in the revenue position and the cost in the profit calculation. This does not accurately reflect the relationship between revenue and costs.
This choice inaccurately reverses the roles of costs and revenue. It suggests that the profit is derived from a cost of lemons (0.75x) being greater than the revenue from lemonade sales (0.50y), which does not make sense in the context of profit calculation. Profit should be the revenue minus the costs, not the other way around.
The accurate equation representing the student's profit from selling lemonade is P = 0.50y - 0.75x. This equation effectively captures the relationship between the revenue from lemonade sales and the costs of lemons purchased, ensuring a correct calculation of overall profit. Understanding this relationship is crucial for effective pricing and cost management in any business venture.
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