the function $f(x)=\frac{30 + 0.25x}{x}$ yields the average cost in dollars per cup of lemonade made by…

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?\nlincoln sells lemonade for 25 cents a cup.\nlincoln gave away 30 cups of lemonade for free.\nlincoln uses 25 cents worth of supplies per cup.\nlincoln uses 30 cents worth of supplies per cup.

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?\nlincoln sells lemonade for 25 cents a cup.\nlincoln gave away 30 cups of lemonade for free.\nlincoln uses 25 cents worth of supplies per cup.\nlincoln uses 30 cents worth of supplies per cup.

Answer

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{30 + 0.25x}{x}$ as $f(x)=\frac{30}{x}+0.25$.

Step2: Analyze the components

The $\frac{30}{x}$ part represents a fixed - cost component spread over $x$ cups, and the $0.25$ represents a per - cup cost. Since the $0.25$ is multiplied by $x$ in the original numerator, it means that for each cup ($x$), there is a cost of 0.25 dollars or 25 cents worth of supplies used.

Answer:

Lincoln uses 25 cents worth of supplies per cup.