Question

A limo company charges $25.50forthefirst8milesplusanadditional$3.50 for each extra mile. What is the cost of a 13-mile limo ride? (A) $29.00(B)$43.00 (C) $45.50(D)$221.50

Short answer

The cost of a 13-mile limo ride is $43.00$.

Step-by-step solution

Determine the number of extra miles

We are told that the limo ride is 13 miles long. The first 8 miles have been accounted for in the initial cost. To find out how many extra miles there are, subtract 8 from 13: $13-8=5$ miles There are 5 extra miles beyond the first 8 miles.

Calculate the charges for the extra miles

The limo company charges $3.50foreachextramile.Sincethereare5extramiles,wewillmultiplythenumberofextramiles(5)bythechargeperextramile($3.50): $5\ast 3.50=17.50$ The charges for the extra 5 miles amount to $17.50.

Calculate the total cost of the 13-mile limo ride

Now we will add the initial charge of $25.50(forthefirst8miles)tothechargefortheextra5miles($17.50): $25.50+17.50=43.00$ The cost of a 13-mile limo ride is $43.00. So the correct answer is (B) $43.00.

Key concepts

Word Problems

Word problems in math are real-life scenarios that you need to solve using mathematical concepts. These problems often describe a situation with words rather than numbers, requiring you to translate the text into a mathematical equation. For instance, in our limo ride problem, the challenge is to find the total cost of a 13-mile trip. Word problems are common in exams like the GED to test your ability to apply math in practical situations.

When approaching a word problem:

• First, understand what the problem is asking. For our limo problem, we are tasked with calculating the cost of a ride over a certain distance.
• Identify important numbers and details. In our example, important details include the cost per mile and the number of total miles.
• Break the problem down into smaller steps. For instance, calculating the cost for extra miles separately.

By following these steps, you can better navigate through any word problem with ease.

Arithmetic Operations

Arithmetic operations are basic calculations that are essential for solving most math problems, including addition, subtraction, multiplication, and division. In the limo company example, we mainly use addition and multiplication to find the solution.

Here's how to apply these operations:

• Subtraction: To find how many extra miles were driven, we subtracted the 8 already covered miles from the total 13 miles directly: $13-8=5$ extra miles.
• Multiplication: Then, we calculated the cost of these extra miles by multiplying them with the per mile cost:$5\times 3.50=17.50$.
• Addition: Finally, to find the total cost, we added the standard cost for the first 8 miles with the cost of the extra miles:$25.50+17.50=43.00$.

The basic operations are like building blocks, helping piece together solutions to more complex problems.

Cost Calculation

Cost calculation involves determining the total expense incurred based on a given rate and quantity. In our example, this process involved multiple steps to compute the limo trip's final expense. Breaking down costs like this is a common real-world application of math and an essential skill for managing personal and business finances.

Here's the process in detail:

• Identify all cost components involved beforehand. The limo company charges two different rates: a base rate for the first segment of the journey and a per-mile rate for extra miles.
• Calculate the fixed cost: In our scenario, the first 8 miles have a set cost of $25.50$.
• Calculate the variable cost per additional unit: Each extra mile is charged at $3.50$. Multiply this rate by the number of extra miles to find the variable cost.
• Combine fixed and variable costs for the total: Add both the sums we calculated to get the full cost of the service. This gives us $43.00$ for 13 miles.

Understanding cost calculations enables us to predict expenses and better plan for future transactions.