Question

Tickets for a train trip sell for the following prices: First-class tickets \(\$ 6.00\) Second-class tickets \(\$ 3.50\) Which of the following expressions represents the average ticket price for all tickets sold if the station sells 110 first-class and 172 second-class tickets? A. \(\frac{110+172}{2}\) B. \(\frac{110(6.00)+172(3.50)}{2}\) C. \(\frac{(110+172)+4.75}{110+172}\) D. \(\frac{110(6.00)+172(3.50)}{110+172}\)

Short answer

The short answer to the question is: D. \[\frac{110(6.00) + 172(3.50)}{110 + 172}\]

Step-by-step solution

1. Calculate the total amount spent on first-class tickets.

Let's calculate the total amount spent on first-class tickets. We multiply the number of first-class tickets sold (110) by the price of a first-class ticket (\(6.00\)): \[110 \times 6.00 = 660.\]

2. Calculate the total amount spent on second-class tickets.

Now, let's calculate the total amount spent on second-class tickets. We multiply the number of second-class tickets sold (172) by the price of a second-class ticket: \[172 \times 3.50 = 602.\]

3. Calculate the total amount spent on all tickets.

Next, let's find the total amount spent on all the tickets, by adding the amount spent on first-class tickets and second-class tickets: \[660 + 602 = 1262.\]

4. Calculate the total number of tickets sold.

We need to find the total number of tickets sold (both first-class and second-class). We sum up the number of first-class tickets sold (110) and the number of second-class tickets sold (172): \[110 + 172 = 282.\]

5. Calculate the average ticket price for all tickets sold.

Finally, we will calculate the average ticket price for all tickets sold by dividing the total amount spent on all tickets by the total number of tickets sold: \[\frac{1262}{282} = 4.475.\] Comparing the result to the given expressions, we find that option D is the correct one: \[\frac{110(6.00) + 172(3.50)}{110 + 172}.\]

Key concepts

First-Class and Second-Class Tickets

Understanding the difference between first-class and second-class tickets is key to solving this kind of problem.

• First-Class Tickets: These are often more expensive due to premium services and comfort. In our example, each first-class ticket costs $6.00.
• Second-Class Tickets: These are usually more economical, providing basic services at a lower cost. Here, each second-class ticket is priced at $3.50.

To average the ticket prices, we need to know how many of each type were sold.

Basic Arithmetic Operations

Basic arithmetic operations are crucial when calculating totals in everyday problems like pricing.

• Multiplication: Used to find the total cost of each type of ticket. For instance, you'll multiply the number of tickets by their respective prices.
• Addition: Helps combine costs and quantities. By adding together all sales, we get the total revenue from tickets.
• Division: Used for averaging. We divide the sum of all ticket sales by the total number of tickets to find the average price.

These operations are the foundation of calculating the average ticket price.

Math Problem Solving

Math problem solving is about applying logical steps to find a solution. Let's break down the solution process:

• Identifying the Problem: Recognize you need the average price of all tickets sold.
• Setting Up the Equation: Use the formula \[\frac{\text{Total Revenue}}{\text{Total Tickets Sold}}\]
• Performing Calculations: Follow the steps to calculate total revenue and the total number of tickets, then divide to find the average.

This structured method helps in finding the correct answer.

GED Test Preparation

Preparing for the GED test requires practice with problems like these. Here’s how you can apply this problem to your study routine:

• Understanding the Concepts: Ensure you grasp each operation and why it's used.
• Practice with Similar Problems: Look for other average pricing scenarios, such as different fares for concerts or events.
• Review Mistakes: If you make an error, review it to understand what went wrong and how to correct it.

Consistent practice with these concepts will boost your confidence and problem-solving skills on test day.