Question

the function ( f(x)=\frac{30 + 0.25x}{x} ) yields the average cost in dollars per cup of lemonade made by lincoln at his lemonade stand when he makes ( x ) cups of lemonade. which statement best fits the situation modeled by the function?

• lincoln sells lemonade for 25 cents a cup.
• lincoln gave away 30 cups of lemonade for free.
• lincoln uses 25 cents worth of supplies per cup.
• lincoln uses 30 cents worth of supplies per cup.

Explanation:

Step1: Recall average cost formula

Average cost $\bar{C}(x) = \frac{\text{Total Cost } C(x)}{x}$

Step2: Expand given average cost function

$$\bar{C}(x) = \frac{30 + 0.25x}{x} = \frac{30}{x} + 0.25$$

Step3: Match to cost components

Total cost $C(x) = 30 + 0.25x$, where $30$ is fixed cost, $0.25x$ is variable cost (cost per cup = $0.25$ dollars = 25 cents).

Answer:

Lincoln uses 25 cents worth of supplies per cup.