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 $2 profit for each hot dog sold. Which equation represents [tex]$y$[/tex], the profit earned by the hot dog stand for [tex]$x$[/tex] hot dogs sold?
A. [tex]y=48 x-2[/tex]
B. [tex]y=48 x+2[/tex]
C. [tex]y=2 x-48[/tex]
D. [tex]y=2 x+48[/tex]
Answer (2)
The profit is a linear function of the number of hot dogs sold.
The revenue from selling x hot dogs is 2 x .
The fixed cost is $48.
The profit y is the revenue minus the cost: y = 2 x − 48 .
Explanation
Problem Analysis Let's analyze the problem. The profit y is a linear function of the number of hot dogs sold x . The owner has a fixed cost of $48 each day, and earns $2 profit for each hot dog sold. We need to find the equation that represents this relationship.
Equation Setup The profit is calculated as the revenue from selling hot dogs minus the cost. The revenue is the profit per hot dog times the number of hot dogs sold, which is 2 x . The cost is a fixed cost of $48. Therefore, the profit y is given by the equation: y = 2 x − 48
Final Equation The equation that represents the profit earned by the hot dog stand for x hot dogs sold is: y = 2 x − 48
Examples
Imagine you're running a lemonade stand. You spend $10 on lemons, sugar, and cups. You sell each cup of lemonade for $1.50. The equation y = 1.50 x − 10 tells you how much profit you'll make ( y ) if you sell x cups of lemonade. This helps you figure out how many cups you need to sell to break even or reach a certain profit goal. Understanding linear functions like this is super useful for managing any small business or even your personal budget!
The profit earned by the hot dog stand can be modeled by the equation y = 2 x − 48 , where y is the profit and x is the number of hot dogs sold. This represents the revenue from hot dogs minus the fixed cost of supplies. The chosen answer is C.
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