To determine the equation that represents [tex]\( y \)[/tex], the profit earned by the hot dog stand for [tex]\( x \)[/tex] hot dogs sold, let's follow the given conditions step-by-step.
1. Understand the fixed cost and profit:
- Fixed cost: The owner spends [tex]\( \$48 \)[/tex] every morning for the supplies. This is a constant expense, regardless of the number of hot dogs sold.
- Profit per hot dog: The owner earns [tex]\( \$2 \)[/tex] profit for each hot dog sold.
2. Form the equation:
- The total revenue from selling [tex]\( x \)[/tex] hot dogs is [tex]\( 2x \)[/tex] dollars, since he earns [tex]\( \$2 \)[/tex] profit per hot dog.
- The fixed cost remains [tex]\( \$48 \)[/tex].
3. Calculate the net profit:
- To calculate the net profit [tex]\( y \)[/tex], we subtract the fixed cost from the total revenue. This can be expressed mathematically as:
[tex]\[
y = 2x - 48
\][/tex]
- Here, [tex]\( 2x \)[/tex] is the revenue from selling [tex]\( x \)[/tex] hot dogs, and [tex]\( 48 \)[/tex] is the fixed daily cost.
Thus, the correct equation representing the profit [tex]\( y \)[/tex] for [tex]\( x \)[/tex] hot dogs sold is:
[tex]\[
y = 2x - 48
\][/tex]
Therefore, the correct answer is:
[tex]\[ y = 2x - 48 \][/tex]
