The numerator of the rational expression [tex]\( \frac{18x + 35}{x} \)[/tex] is [tex]\( 18x + 35 \)[/tex]. Let's break down what this numerator represents in the context of the guided tour organized by Jessica.
1. Variable Part (18x):
- This part, [tex]\( 18x \)[/tex], represents the profit that depends on the number of people, [tex]\( x \)[/tex], going on the tour.
- Specifically, for each person (per person) joining the tour, the company makes a profit of 18 units (which could be in dollars or any other currency).
2. Constant Part (35):
- This part, [tex]\( 35 \)[/tex], represents a fixed profit that does not depend on the number of people.
- This could be a base profit the company expects to make regardless of how many people participate.
Combining these two parts, the numerator [tex]\( 18x + 35 \)[/tex] represents the total profit from [tex]\( x \)[/tex] people going on the tour. This total profit is composed of:
- A variable part [tex]\( 18x \)[/tex], which scales with the number of participants.
- A constant part 35, which remains the same regardless of the number of participants.
So, the numerator [tex]\( 18x + 35 \)[/tex] of the rational expression [tex]\( \frac{18x + 35}{x} \)[/tex] represents the total profit from [tex]\( x \)[/tex] people, consisting of a variable part 18x and a constant part 35.
