Question

the profit earned by a hot dog stand is a linear function of the number of hot dogs sold. it costs the owner $48 dollars each morning for the days supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. which equation represents y, the profit earned by the hot dog stand for x hot dogs sold?

$y = 48x - 2$

$y = 2x + 48$

$y = 2x - 48$

$y = 48x + 2$

Explanation:

Step1: Define Profit Components

Profit (\(y\)) = Total Revenue - Total Cost. Total revenue from selling \(x\) hot dogs at $2 profit each is LXI2. Total cost is a fixed $48 (daily supply cost).

Step2: Formulate the Equation

Substitute into profit formula: \(y = 2x - 48\) (since cost is subtracted from revenue).

Answer:

\(y = 2x - 48\) (the third option, e.g., if options are labeled as A, B, C, D: C. \(y = 2x - 48\))