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The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner [tex]$48 each morning for the day's supply of hot dogs, buns, and mustard, but he earns $[/tex]2 profit for each hot dog sold.

Which equation represents [tex]\( y \)[/tex], the profit earned by the hot dog stand for [tex]\( x \)[/tex] hot dogs sold?

A. [tex]\( y = 48x - 2 \)[/tex]
B. [tex]\( y = 48x + 2 \)[/tex]
C. [tex]\( y = 2x - 48 \)[/tex]
D. [tex]\( y = 2x + 48 \)[/tex]



Answer :

GinnyAnswer
To determine the correct equation that represents the profit earned by the hot dog stand for [tex]\( x \)[/tex] hot dogs sold, we need to break down the problem and consider the given information step-by-step.

1. Daily Cost:
The fixed daily cost to run the hot dog stand is \[tex]$48. This is a fixed expense independent of the number of hot dogs sold. 2. Profit per Hot Dog: The profit per hot dog sold is \$[/tex]2. This means for each hot dog sold, the profit increases by \$2.

3. Formulating the Profit Equation:
- The total earnings from selling [tex]\( x \)[/tex] hot dogs can be calculated as [tex]\( 2x \)[/tex] dollars.
- The total profit, [tex]\( y \)[/tex], is given by the total earnings minus the daily cost. Therefore,

[tex]\[ y = 2x - 48 \][/tex]

This equation indicates that the profit earned [tex]\( y \)[/tex] is a linear function of the number of hot dogs sold [tex]\( x \)[/tex], where:
- [tex]\( 2x \)[/tex] represents the revenue generated from selling [tex]\( x \)[/tex] hot dogs
- [tex]\( 48 \)[/tex] represents the fixed daily cost that needs to be subtracted from the revenue to get the profit.

4. Conclusion:
The correct equation that represents the profit earned by the hot dog stand for [tex]\( x \)[/tex] hot dogs sold is:

[tex]\[ y = 2x - 48 \][/tex]

Thus, the correct answer is:

[tex]\[ y = 2x - 48 \][/tex]

This matches the third option in the list:

[tex]\[ y = 2x - 48 \][/tex]

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