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Chapter 1: Problem 25

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

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

Step by step solution

01

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 (\(6.00\)): \[110 \times 6.00 = 660.\]
02

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: \[172 \times 3.50 = 602.\]
03

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: \[660 + 602 = 1262.\]
04

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): \[110 + 172 = 282.\]
05

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: \[\frac{110(6.00) + 172(3.50)}{110 + 172}.\]

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