How to Determine Total Toll Costs from Miles Driven
Quick Answer
To calculate total toll costs based on miles driven, use the formula y = 0.37x + 5. For example, driving 75 miles results in a toll cost of approximately $30.75.
Understanding how to calculate toll costs based on miles driven is essential for budgeting your travel expenses. The formula we are using is given by the line of best fit:
$$y = 0.37x + 5$$
In this equation, $x$ represents the number of miles you drive, and $y$ is the total toll cost in dollars. The constant $5$ indicates that there is a minimum toll cost of $5, even if you drive zero miles. This means that any statement suggesting you can spend less than $5 for any distance is incorrect and provides a useful clue for evaluating options.
Let's break down the formula further to understand how to use it effectively. The slope, $0.37$, tells us that for every mile you drive, the toll increases by $0.37. This is slightly more than a third of a dollar, which helps us estimate costs quickly. For instance, if you drive 75 miles, you can calculate the toll as follows:
1. Plug in $x = 75$ into the formula:
$$y = 0.37(75) + 5$$
2. Calculate $0.37 imes 75$, which gives you approximately $27.75$.
3. Now, add the fixed cost of $5$:
$$y = 27.75 + 5 = 32.75$$
Thus, the total toll cost for driving 75 miles is approximately $32.75, which is indeed over $30. This means that any claim stating you can spend less than $30 to go 75 miles is incorrect.
Let’s explore a few more examples to solidify your understanding.
- **Example 1**: If you drive 100 miles, what would your toll cost be?
1. Plug in $x = 100$:
$$y = 0.37(100) + 5$$
2. Calculate:
$$y = 37 + 5 = 42$$
The total cost for 100 miles is $42.
- **Example 2**: What about 50 miles?
1. Plug in $x = 50$:
$$y = 0.37(50) + 5$$
2. Calculate:
$$y = 18.5 + 5 = 23.5$$
So, the toll cost for 50 miles is $23.50.
In real-world applications, knowing how to calculate toll costs can help you plan your travel budget better. It's also useful for understanding how different distances will affect your total expenses on trips. Always remember to check for any fixed fees or minimum costs when using such formulas in practical scenarios.
By practicing these calculations, you’ll become more confident in handling similar problems in the future.
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