Problem 15 - Algebra A Combined Function

Question

A car rental agency advertised renting a Buick Century for \(\$ 24.95\) per day and \(\$ 0.29\) per mile. If you rent this car for 2 days, how many whole miles can you drive on a \(\$ 100\) budget?

Step-by-Step Solution

Answer

You can drive 172 whole miles.

Step 1: Calculate Daily Cost

Determine the total cost for renting the car for 2 days. The rental cost per day is \( \\(24.95 \), so for 2 days, the total daily cost is \( \\)24.95 \times 2 = \$49.90 \).

Step 2: Calculate Amount for Miles

Subtract the total daily rental cost from the budget to find out how much money is left for the mileage costs. The budget is \( \\(100 \), so the amount left is \( \\)100 - \\(49.90 = \\)50.10 \).

Step 3: Calculate the Number of Miles

Determine how many miles you can drive with \\(50.10. Since the cost per mile is \( \\)0.29 \), divide the remaining money by the cost per mile: \( \frac{\\(50.10}{\\)0.29} \approx 172.75 \).

Step 4: Determine Whole Miles

Since you can't drive a fraction of a mile, you round down to the nearest whole number. Thus, you can drive a total of 172 whole miles.

Key Concepts

Cost per Mile

When budgeting for a car rental, understanding the cost per mile is crucial. This cost is the additional amount you pay for every mile you drive the rental car. In the provided problem, the cost per mile is set at \(\\(0.29\). It’s essential to note that this cost is variable and will depend on how many miles you drive.

To calculate your mileage cost, multiply the number of miles you plan to drive by the cost per mile. For instance, if you drive 100 miles, your mileage cost would be \(100 \times 0.29 = \\)29\). Recognizing this aspect helps in effective budgeting, ensuring you don't overspend or miscalculate your rental expenses.

Daily Rental Cost

The daily rental cost is the fixed amount you pay per day for using the car. In many rental agreements, this cost is applied regardless of how many miles you drive. For the Buick Century, the daily rental cost is \(\\(24.95\) per day.

This expense is straightforward but needs to be multiplied by the number of days you plan to have the rental. In the problem, renting the car for 2 days results in a total daily rental cost of \(2 \times 24.95 = \\)49.90\). Knowing your daily rental cost helps you budget for the minimum amount you need just to keep the car for the required duration.

Calculating Expenses

Calculating expenses for a car rental involves adding the daily rental costs to the estimated mileage costs. First, determine your budget and then subtract the fixed daily rental cost from it. This will show how much money remains for driving the car extra miles.

For example, if you have a budget of \(\\(100\) and your fixed rental cost for 2 days is \(\\)49.90\), then you have \(\\(100 - \\)49.90 = \$50.10\) left. This leftover amount will be used solely for mileage charges. Therefore, it’s essential to calculate all expenses upfront to avoid unexpected charges later.

Whole Number Rounding

When calculations involve fractional numbers, especially with physical quantities like miles, rounding to the nearest whole number becomes necessary. In this problem, you calculated that \(\$50.10\) allows you to drive approximately 172.75 miles. However, you can't drive a fraction of a mile with standard vehicles.

Thus, you round down to the nearest whole number to ensure that your mileage fits within the budget. So, you end up with 172 whole miles. Always rounding down guarantees that you won’t exceed your budget or contractual limitations from the rental company.