Question

interpreting rational expressions
this activity will help you meet these educational goals:
you will interpret the meaning of specific parts of real - world rational expressions and manipulate rational expressions to extract additional contextual information.
directions
read the instructions for this self - checked activity. type in your response to each question, and check your answers. at the end of the activity, write a brief evaluation of your work.
activity
read the following scenario, and answer the questions that follow.
jessica is organizing a guided tour of the rain forest. the average profit per person that the touring company makes is given by the rational expression (\frac{18x + 35}{x}), where (x) is the number of people going on the tour.
part a
what does the numerator of this rational expression represent?

Explanation:

Step1: Recall the meaning of average profit formula

The formula for average profit per person is \(\text{Average Profit}=\frac{\text{Total Profit}}{\text{Number of People}}\). Here, the average profit per person is given by \(\frac{18x + 85}{x}\), where \(x\) is the number of people.

Step2: Analyze the numerator

In the formula \(\text{Average Profit}=\frac{\text{Total Profit}}{\text{Number of People}}\), the numerator corresponds to the total profit. So, for the rational expression \(\frac{18x + 85}{x}\), the numerator \(18x+85\) should represent the total profit the touring company makes from the tour. We can think of it as the sum of two parts: maybe a variable cost - related part (\(18x\)) and a fixed cost or additional revenue part (85), but overall, in the context of average profit (total profit divided by number of people), the numerator is the total profit.

Answer:

The numerator \(18x + 85\) of the rational expression \(\frac{18x + 85}{x}\) represents the total profit that the touring company makes from the rain forest tour, where \(x\) is the number of people going on the tour. This is because the average profit per person is calculated as total profit divided by the number of people, so the numerator corresponds to the total profit (the sum of all profits from the \(x\) people, which can be thought of as having a component related to the number of people (\(18x\)) and a fixed or additional component (85)).