A Taxi Service Charges A Flat Fee Of $\$1.25$ And $\$0.75$ Per Mile. If Henri Has $\$14.00$, Which Of The Following Shows The Number Of Miles He Can Afford To Ride In The Taxi?A. $m \leq 17$ B. $m \geq 17$

Introduction

When it comes to taxi services, pricing can be a complex issue. Many taxi services charge a flat fee, in addition to a per-mile charge. In this article, we will explore a pricing problem involving a taxi service that charges a flat fee of $\$1.25$ and $\$0.75$ per mile. We will use mathematical equations to determine the number of miles a customer can afford to ride in the taxi, given a certain amount of money.

Problem Statement

Henri has $\$14.00$ to spend on a taxi ride. The taxi service charges a flat fee of $\$1.25$ and $\$0.75$ per mile. We need to find the number of miles Henri can afford to ride in the taxi.

Mathematical Model

Let $m$ be the number of miles Henri can afford to ride in the taxi. The total cost of the taxi ride can be represented by the equation:

$$Total\ Cost = Flat\ Fee + (Per\ Mile\ Charge \times Number\ of\ Miles)$$

Substituting the given values, we get:

$$Total\ Cost = \$1.25 + (\$0.75 \times m)$$

Since Henri has $\$14.00$ to spend, we can set up the inequality:

$$\$1.25 + (\$0.75 \times m) \leq \$14.00$$

Solving the Inequality

To solve the inequality, we need to isolate the variable $m$. First, we subtract $\$1.25$ from both sides of the inequality:

$$\$0.75 \times m \leq \$12.75$$

Next, we divide both sides of the inequality by $\$0.75$:

$$m \leq \frac{\$12.75}{\$0.75}$$

Calculating the Number of Miles

To calculate the number of miles Henri can afford to ride in the taxi, we need to evaluate the expression:

$$m \leq \frac{\$12.75}{\$0.75}$$

Using a calculator, we get:

$$m \leq 17$$

Conclusion

Based on the mathematical model and the inequality, we can conclude that Henri can afford to ride in the taxi for at most $\boxed{17}$ miles.

Discussion

The problem presented in this article is a classic example of a linear inequality. The solution involves isolating the variable $m$ and evaluating the expression. The result shows that Henri can afford to ride in the taxi for at most 17 miles.

Comparison of Options

Let's compare the result with the given options:

A. $m \leq 17$ B. $m \geq 17$

Based on the calculation, we can see that option A is the correct answer.

Limitations of the Model

The mathematical model presented in this article assumes that the taxi service charges a flat fee and a per-mile charge. However, in reality, taxi services may have different pricing structures. Additionally, the model does not take into account other factors that may affect the cost of the taxi ride, such as traffic, tolls, and tips.

Future Research Directions

Future research directions may include:

• Developing a more realistic mathematical model that takes into account different pricing structures and other factors that may affect the cost of the taxi ride.
• Investigating the impact of different pricing structures on the number of miles a customer can afford to ride in the taxi.
• Developing a decision-making framework that helps customers make informed decisions about their taxi rides.

References

• [1] "Taxi Service Pricing: A Review of the Literature." Journal of Transportation Economics, vol. 10, no. 2, 2018, pp. 123-145.
• [2] "The Impact of Pricing Structures on Taxi Service Demand." Journal of Transportation Research, vol. 25, no. 1, 2020, pp. 1-15.

Note: The references provided are fictional and for demonstration purposes only.