- The total cost consists of a fixed base fee of \(\$5\) and a variable cost of \(\$1.50\) per mile (\(m\)).
- The mathematical expression for the total cost is \(\$1.5m + 5\).
- Since the total cost is \(\$35\), the correct equation is \(1.5m + 5 = 35\).
- Final answer: \(\boxed{1.5m + 5 = 35}\)
Explanation
- Analysis of the Situation
To determine the correct equation, we identify the components of the total cost for the taxi ride. We are given a fixed base fee of \(\$5\) and a variable rate of \(\$1.50\) per mile traveled. Let \(m\) be the number of miles traveled. The total cost is calculated by summing the fixed fee and the product of the rate per mile and the number of miles, which is given by \(1.5 \times m + 5\). Since the total amount paid by Kyle is \(\$35\), we set this expression equal to 35.
- Formulating and Selecting the Equation
We express the total cost as the sum of the fixed base fee and the variable fee based on the number of miles \(m\). The cost for the distance traveled is \(1.5 \times m\) and the base fee is \(5\). Therefore, the total cost for the trip is \(\$1.5m + 5\). According to the problem, the total cost paid by Kyle is \(\$35\). Equating these, we obtain the equation:
\[1.5m + 5 = 35\]
Comparing this result with the provided options, it matches the third option.
Examples
This type of linear modeling is essential for everyday financial calculations, such as determining taxi fares, utility bills, or planning a budget based on fixed and variable costs. Understanding how to translate word problems into algebraic equations allows you to solve for unknown variables, such as the distance you can travel on a set budget, ensuring you can manage your resources effectively. For example, if you have a specific amount of money and want to know how many hours of a service you can afford, you can set up a similar equation to find the exact value.