Answer :
Sure! Let's take a closer look at the given expression and understand what each part represents.
The expression provided is:
[tex]\[
\frac{150x}{x+4} + 250
\][/tex]
Here, [tex]\(x\)[/tex] represents the number of senior citizens who travel by the company's cabs. We want to understand what the constant term "250" signifies in the context of this expression.
### Step-by-Step Explanation:
1. Understanding the Expression:
- The expression models the average amount a cab driver collects on a particular day.
- The part [tex]\(\frac{150x}{x+4}\)[/tex] varies with the number of senior citizens [tex]\(x\)[/tex] traveling.
- The constant "+ 250" is added to this varying part.
2. Evaluating the Constant Term:
- A constant in an expression does not depend on [tex]\(x\)[/tex]. Here, 250 is not affected by the number of senior citizens traveling.
- To explore the role of the constant, consider the scenario when no senior citizens travel (i.e., [tex]\(x = 0\)[/tex]).
3. When [tex]\(x = 0\)[/tex] (no senior citizens travel):
- Substituting [tex]\(x = 0\)[/tex] into the expression:
[tex]\[
\frac{150 \times 0}{0+4} + 250 = \frac{0}{4} + 250 = 0 + 250 = 250
\][/tex]
- This calculation shows that when no senior citizens travel, the average amount collected by a cab driver is exactly 250.
4. Interpreting the Result:
- Therefore, the constant term "250" represents the average amount a cab driver collects when no senior citizens use the cabs.
Given these steps, the correct interpretation of the constant term is:
A. The constant 250 represents the average amount a cab driver collects on a particular day when no senior citizens travel by the company's cabs.
The expression provided is:
[tex]\[
\frac{150x}{x+4} + 250
\][/tex]
Here, [tex]\(x\)[/tex] represents the number of senior citizens who travel by the company's cabs. We want to understand what the constant term "250" signifies in the context of this expression.
### Step-by-Step Explanation:
1. Understanding the Expression:
- The expression models the average amount a cab driver collects on a particular day.
- The part [tex]\(\frac{150x}{x+4}\)[/tex] varies with the number of senior citizens [tex]\(x\)[/tex] traveling.
- The constant "+ 250" is added to this varying part.
2. Evaluating the Constant Term:
- A constant in an expression does not depend on [tex]\(x\)[/tex]. Here, 250 is not affected by the number of senior citizens traveling.
- To explore the role of the constant, consider the scenario when no senior citizens travel (i.e., [tex]\(x = 0\)[/tex]).
3. When [tex]\(x = 0\)[/tex] (no senior citizens travel):
- Substituting [tex]\(x = 0\)[/tex] into the expression:
[tex]\[
\frac{150 \times 0}{0+4} + 250 = \frac{0}{4} + 250 = 0 + 250 = 250
\][/tex]
- This calculation shows that when no senior citizens travel, the average amount collected by a cab driver is exactly 250.
4. Interpreting the Result:
- Therefore, the constant term "250" represents the average amount a cab driver collects when no senior citizens use the cabs.
Given these steps, the correct interpretation of the constant term is:
A. The constant 250 represents the average amount a cab driver collects on a particular day when no senior citizens travel by the company's cabs.
