/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 Yesterday the Hess Mart at the j... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 13

Yesterday the Hess Mart at the junction of state highways 707 and 544 in Socastee, South Carolina sold 3,265 gallons of gasoline to motorists. They offered unleaded regular at \(\$ 1.749\) per gallon, unleaded plus at \(\$ 1.849\) per gallon, and unleaded supreme at \(\$ 1.949\) per gallon. Of the total gallons sold, 80.2 percent was unleaded regular, 15.2 percent unleaded plus, and the remaining 4.6 percent was unleaded supreme. Find the weighted mean selling price.

Short Answer

Expert verified
The weighted mean selling price is $1.772 per gallon.

Step by step solution

01

Calculate Total Gallons for Each Type of Gasoline

First, we need to determine how many gallons of each type of gasoline were sold. **Unleaded Regular:** 80.2% of 3,265 gallons = 0.802 * 3,265 = 2,619.73 gallons **Unleaded Plus:** 15.2% of 3,265 gallons = 0.152 * 3,265 = 496.28 gallons **Unleaded Supreme:** 4.6% of 3,265 gallons = 0.046 * 3,265 = 149.19 gallons
02

Calculate Total Revenue for Each Type of Gasoline

Now, calculate the revenue from each type by multiplying the price per gallon by the number of gallons sold.**Unleaded Regular Revenue:** \( 2,619.73 \text{ gallons} \times 1.749 \text{ per gallon} = \\( 4,577.65\) **Unleaded Plus Revenue:** \( 496.28 \text{ gallons} \times 1.849 \text{ per gallon} = \\) 917.78 \) **Unleaded Supreme Revenue:** \( 149.19 \text{ gallons} \times 1.949 \text{ per gallon} = \$ 290.63 \)
03

Calculate Total Revenue and Total Gallons Sold

Add the revenues calculated in Step 2 to get the total revenue, and ensure your total gallons match the original problem statement.**Total Revenue:**\( 4,577.65 + 917.78 + 290.63 = \$ 5,786.06 \) **Total Gallons Sold:**\( 2,619.73 + 496.28 + 149.19 = 3,265 \text{ gallons} \) (Matches the problem statement).
04

Calculate the Weighted Mean Selling Price

The weighted mean selling price is calculated by dividing the total revenue by the total gallons sold. This will give us the average price paid per gallon.\[ \text{Weighted Mean Price} = \frac{5,786.06}{3,265} = 1.772 \text{ per gallon} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Revenue Calculation
Understanding how to calculate revenue is essential, especially when dealing with gasoline sales. Revenue refers to the total income generated from selling products or services. In this scenario, revenue is calculated by multiplying the number of gallons sold by the price per gallon for each type of gasoline offered at the Hess Mart.
For example, to determine the revenue from selling unleaded regular gasoline, calculate:
  • Multiply the number of unleaded regular gallons by its price per gallon.
  • Thus, revenue from unleaded regular is \(2,619.73 \text{ gallons} \times \\(1.749 = \\)4,577.65\).
Repeating this for each gasoline type provides the total revenue generated from gasoline sales.
Percentage
Percentage helps in understanding proportions and is crucial in breaking down total sales into types of gasoline. In this problem, percentages are used to figure out how much of each gasoline type was sold from a total of 3,265 gallons.
The exercise shows how to convert percentages into actual figures:
  • Multiply the total gallons by the percentage (in decimal form) for each gasoline type.
  • For example, to find gallons of unleaded regular, convert 80.2% to decimal format \(0.802\) and multiply by \(3,265\).
  • This results in 2,619.73 gallons.
Percentages like these are powerful tools for interpreting data.
Gasoline Sales
Selling gasoline involves understanding various factors such as types, percentages, and prices. At the Hess Mart, three types of gasoline were sold: unleaded regular, unleaded plus, and unleaded supreme. Different types generally have different prices depending on their quality and octane levels, and customers choose according to preference and cost considerations.
The percentage breakdown of sales reveals consumer preferences, with a majority purchasing unleaded regular.
  • Unleaded Regular: 80.2% of purchases
  • Unleaded Plus: 15.2%
  • Unleaded Supreme: 4.6%
The exercise translates these preferences into concrete sales figures, illustrating the importance of gasoline type in total sales.
Step-by-Step Solution
Following a step-by-step solution is a structured way of solving complex problems, such as finding the weighted mean selling price of gasoline. Each step builds upon the previous one to ensure accuracy. Here鈥檚 how it was tackled:
  • First, the number of gallons sold for each type of gasoline was determined using percentages.
  • Next, the revenue from each type was calculated by multiplying the gallons by their respective prices.
  • A sum of all revenues gave the total revenue, and verifying total gallons confirmed these calculations.
  • The weighted mean price, providing an average price per gallon, was then calculated by dividing total revenue by total gallons.
This careful breakdown allows a complex calculation to become manageable and understandable.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

There are many financial websites that provide information on stocks by industry. For example, go to http://biz.yahoo.com and select Stock Research; under Analyst Research select Sector/Industry. There are many choices available here such as Energy, Financial, and Healthcare. Select one of these sectors, such as Healthcare. Another list of choices is now available; select one such as Major Drug. A list of companies in that industry will appear. Select one of the variables available, such as the price to earnings ratio, listed as \(\mathrm{P} / \mathrm{E}\). This variable is the ratio of the selling price of a share of the company's common stock to the earnings per share of common stock. Download this information into Excel and find the mean, median, and standard deviation. Go back to Sector/Industry and choose another Sector and Industry. You might want to select Energy and then Coal. A list of companies will appear. Select the same variable as before. Download the information to Excel and find the mean, median, and standard deviation for this industry. Compare the information on the two sectors. Write a brief report summarizing your findings. Are the means different? Is there more variability in one industry than another?

The following five values are a sample: \(11,6,10,6,\) and 7 . a. Compute the sample variance. b. Determine the sample standard deviation.

The Consumer Price Index is reported monthly by the U.S. Bureau of Labor Statistics. It reports the change in prices for a market basket of goods from one period to another. The index for 1992 was 140.3 , by 2003 it increased to 184.6 . What was the geometric mean annual increase for the period?

Rolland Poust is a sophomore in the College of Business at Scandia Tech. Last semester he took courses in statistics and accounting, 3 hours each, and earned an \(\mathrm{A}\) in both. He earned a \(B\) in a five-hour history course and a \(B\) in a two-hour history of jazz course. In addition, he took a one- hour course dealing with the rules of basketball so he could get his license to officiate high school basketball games. He got an \(\mathrm{A}\) in this course. What was his GPA for the semester? Assume that he receives 4 points for an \(A, 3\) for a \(B,\) and so on. What measure of location did you just calculate?

Referring to Exercise \(39,\) the annual report of Dennis Industries also gave these returns on stockholder equity for the same five-year period (in percent): \(13.2,5.0,10.2,17.5,\) and \(12.9 .\) a. What is the arithmetic mean return? b. What is the variance?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.