Question

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 = -0.75x - 0.50y \\) \\( p = 0.50y - 0.75x \\) \\( p = 0.75y - 0.50x \\) \\( p = 0.50x - 0.75y \\)

Explanation:

Step1: Define Cost and Revenue

Cost (C) from buying lemons: Each lemon is $0.75, and she buys x lemons, so \( C = 0.75x \).
Revenue (R) from selling cups: Each cup is $0.50, and she sells y cups, so \( R = 0.50y \).

Step2: Calculate Profit

Profit (P) is Revenue minus Cost: \( P = R - C \).
Substitute R and C: \( P = 0.50y - 0.75x \).

Answer:

\( P = 0.50y - 0.75x \) (the second option)