To determine which equation represents [tex]\( y \)[/tex], the profit earned by the hot dog stand for [tex]\( x \)[/tex] hot dogs sold, let's break down the problem step-by-step:
1. Initial Cost:
The owner spends \[tex]$48 each morning for the day's supply of hot dogs, buns, and mustard. This is a fixed cost that reduces the profit. Thus, the profit starts at \(-\$[/tex]48\).
2. Profit per Hot Dog:
The owner earns \[tex]$2 profit for each hot dog sold. Hence, for each hot dog sold, the profit increases by \$[/tex]2.
3. Formulating the Equation:
- Let [tex]\( x \)[/tex] be the number of hot dogs sold.
- The total profit earned from selling [tex]\( x \)[/tex] hot dogs is [tex]\( 2x \)[/tex] dollars because each hot dog sold contributes \[tex]$2 to the profit.
- Since there is an initial cost of \$[/tex]48, this amount must be subtracted from the total profit.
Putting these points together, the profit equation can be set up as follows:
[tex]\[ y = 2x - 48 \][/tex]
Where:
- [tex]\( y \)[/tex] is the total profit.
- [tex]\( 2x \)[/tex] represents the profit from selling [tex]\( x \)[/tex] hot dogs.
- The [tex]\(-48\)[/tex] represents the initial fixed cost.
Therefore, the correct equation is:
[tex]\[ y = 2x - 48 \][/tex]
So, the correct choice is the third one.
