Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

For her first 3 years with a company, Marissa earned $$\$ 45,200$$ each year. For the next 5 years she earned $$\$ 55,400$$ per year. What was the average amount that Marissa earned per year over the 8-year period? A. $$\$ 49,075$$ B. $$\$ 50,300$$ C. $$\$ 51,575$$ D. $$\$ 52,100$$

Short Answer

Expert verified
\(Total \ earnings \ for \ first \ 3 \ years = (45,200) \times (3) = 135,600\) \(Total \ earnings \ for \ next \ 5 \ years = (55,400) \times (5) = 277,000\) \(Total \ earnings \ over \ 8 \ years = (135,600) + (277,000) = 412,600\) \(Average \ annual \ earnings = \frac{412,600}{8} = 51,575\) The correct answer is C. \( \$ 51,575\)

Step by step solution

01

Calculate earnings for the first 3 years

First, we need to find the total earnings for Marissa during her first 3 years with the company. Since she earned $$\$ 45,200$$ each year, we can calculate her total earnings by multiplying her annual earnings by 3: Total earnings for first 3 years = (Annual earnings) × (Number of years) = ($$45,200$$) × (3)
02

Calculate earnings for the next 5 years

Next, we need to find the total earnings for Marissa during the next 5 years with the company. Since she earned $$\$ 55,400$$ each year, we can calculate her total earnings by multiplying her annual earnings by 5: Total earnings for next 5 years = (Annual earnings) × (Number of years) = ($$55,400$$) × (5)
03

Calculate total earnings over 8 years

Now that we have the total earnings for both periods, we can find the overall total earnings for Marissa over the 8-year period by adding the earnings from the two periods: Total earnings over 8 years = (Total earnings for first 3 years) + (Total earnings for next 5 years)
04

Calculate the average annual earnings

To find the average amount Marissa earned per year, we will divide her total earnings over the 8-year period by the number of years, 8: Average annual earnings = (Total earnings over 8 years) / (Number of years) = (Total earnings over 8 years) / (8)
05

Compare the result with the given options

Finally, we will compare our calculated average annual earnings with the given options (A, B, C, and D) to identify the correct answer.

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 Vaia!

Key Concepts

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

Average Annual Earnings Calculation
Understanding how to calculate average annual earnings is crucial for various financial assessments, including salary negotiations, job evaluations, and personal financial planning. In the context of a GED Mathematics test, mastering this calculation can often solve questions related to income over different periods.

To calculate average annual earnings, you must total all the earnings received over a given period and then divide by the number of years in that period. This concept is rooted in the mean, which is a basic statistical measure representing the central value of a data set.

Using Marissa's example, we combine her earnings from different periods of her employment to compute her total earnings. Then, dividing by the total number of years she's been working, we get her average annual earnings. This method shows students the practical use of averages and provides them with skills they can use beyond the classroom.
GED Prep Math Problems
Preparing for the GED Mathematics test involves tackling a variety of math problems that test your quantitative reasoning and problem-solving abilities. Problems like calculating average annual earnings are typical on the GED, as they mix real-world scenarios with the need to apply basic mathematical operations.

To effectively prepare for these problems, it's important to understand not just the basic math operations—addition, subtraction, multiplication, and division—but also how to apply them in practical contexts. Practice problems and textbooks often frame these operations within everyday situations to make them more relatable and to improve understanding.

For GED prep, focusing on step-by-step solutions encourages a thorough understanding of the process behind each answer, which is more beneficial than simply memorizing formulas or numbers. It's about cultivating a mindset of analytical thinking and logical reasoning, which is crucial for success on the GED and future mathematical challenges.
Mathematical Problem-Solving
Mathematical problem-solving entails more than just performing calculations; it's about understanding the situation, figuring out which mathematical operations to use, and applying these operations in the right order. It's a core competency for educational success and an essential skill in many career paths.

In solving the example problem, the process begins with a clear comprehension of the problem statement. Next, we break down the problem into smaller, manageable parts—calculating Marissa's earnings in different intervals and then combining these to find a total. The final step involves averaging this total over the years worked.

Key strategies in mathematical problem-solving include identifying relevant information, selecting the right tools and formulas, and checking whether the solution makes sense in the context of the problem. Encouraging students to explain their reasoning, as done in a step-by-step approach, solidifies their understanding and equips them with the ability to tackle a wide range of mathematical problems.

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

Considering only these 5 bird types, what was the total percentage increase in sightings from 2008 to 2009? (Round your answer to the nearest integer.) A. 7% B. 8% C. 14% D. 18%

A small copy shop spent \(24 \%\) of its monthly revenue on supplies, \(17 \%\) on renting the building, and \(33 \%\) on payroll and taxes. If after paying these expenses, $$\$ 7,384$$ dollars in profit is left, then how much did the copy shop spend on rent? A. $$\$ 3,976$$ B. $$\$ 4,828$$ C. $$\$ 19,198$$ D. $$\$ 28,400$$

A particular aircraft has a mass of 1,800 kilograms, and has engines that provide 90,000 Newtons of thrust force. A second aircraft has a mass of only 1,500 kilograms, but has engines that provide exactly the same acceleration. What amount of thrust force do that aircraft's engines provide? You may use a calculator. Force \([\) Newtons \(]=\) mass \([\) kilograms \(] \times\) acceleration [meters/second \({ }^2\) ] A. 50 Newtons B. 60 Newtons C. 75,000 Newtons D. 108,000 Newtons

The following is a quote by President Abraham Lincoln: "A majority held in restraint by constitutional checks and limitations, and always changing easily with deliberate changes of popular opinions and sentiments, is the only true sovereign of a free people." The above quote most closely describes which of the following forms of government? A. a constitutional republic B. a monarchy C. a pure democracy D. anarchy

Each number below is a possible solution for \(2 x^2-3 \leq\) \(15-x\) EXCEPT A. -3 B. 0 C. 1 D. 3

See all solutions

Recommended explanations on English Textbooks

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.

Sign-up for free