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 day’s 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?

Question

y=48x−2
y=48x+2
y=2x−48
y=2x+48

Answer 1

To determine the equation that represents the profit \( y \) earned by the hot dog stand for \( x \) hot dogs sold, we need to consider both the costs and the earnings.

1. The cost of the daily supply of hot dogs, buns, and mustard is $48. This is a fixed cost, so it does not depend on the number of hot dogs sold.
2. The profit earned from each hot dog sold is $2. Therefore, if \( x \) hot dogs are sold, the total profit from selling those hot dogs would be \( 2x \).

The total profit \( y \) can be calculated by taking the total earnings from selling \( x \) hot dogs and subtracting the fixed cost: \[ y = \text{Total Earnings} - \text{Cost} \] \[ y = 2x - 48 \]

So, the correct equation that represents the profit earned by the hot dog stand for \( x \) hot dogs sold is: \[ \boxed{y = 2x - 48} \]