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Int Algebra: Finding an Average

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About this Lesson

  • Type: Video Tutorial
  • Length: 4:13
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 45 MB
  • Posted: 12/02/2008

This lesson is part of the following series:

College Algebra: Full Course (258 lessons, $198.00)
College Algebra: Equations & Inequalities (50 lessons, $65.34)
Intermediate Algebra Review (25 lessons, $49.50)
College Algebra: Linear Equation Word Problems 1 (10 lessons, $13.86)

In this lesson, you will learn how to approach word problems that involve averages or means. To solve these word problems, you'll go through a prescribed method in which you read the question, define the variables, write the equation and then solve the equation. This is a great lesson to watch to get a feel for how to solve word problems that involve averages or means (many of which include grades or scores).

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Intermediate Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/intermediatealgebra. The full course covers real numbers, equations and inequalities, exponents and polynomials, rational expressions, roots and radicals, relations and functions, the straight line, systems of equations, quadratic equations and quadratic inequalities, conic sections, inverse and exponential and logarithmic functions, and a variety of other AP algebra and advanced algebra.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

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Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

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Equations and Inequalities
More Applications
Finding an Average Page [1 of 1]
Okay, another real world exactly that sometimes comes up in life is the following: someone is desperately studying for
that last exam and hoping of the grade. And so you can just imagine what it looks like. The person just falls asleep in
the textbook and, while they're falling asleep in that textbook, they start dreaming. They start saying, “Gee whiz, I got
an 80 on the first test, an 82 on the second test, a 94, but then a 71 and there’s that one more test.” And that poor
person’s trying so hard to get an 85 average. That’s all he wants. “I just want a B, maybe a B+, if the teacher is a
little bit lenient. That’s all I want out of life. What do I have to get on this test, in order to get an 85 final average?”
That’s the question that our hero dreams about, while he’s trying to study and falls asleep.
All right, let’s think about this together and see if we can make some progress on this. Well, what would you do?
Well, we know that there are going to be five grades; there’s an 82, there’s an 82, there’s a 94, there’s a 71, and then
there’s a mystery grade. That’s the one that hasn’t happened yet. And what do I know? I want the average of all five
of these exams to equal 85. And the question is what kind of grade would our hero have to get on this last exam, in
order to have an average of 85? Well, in fact, if you write it out like this, it really just leads right to what you want to
do, because what do I want to do? I want to compute the average. How do you compute an average? You add up all
the numbers that you have and divide by the number of numbers. In this case, we’ll have 1, 2, 3, 4 and the last one is
5. So we’ll divide by 5.
So what do we see? Well, I’ll set up the following equation and, just to show you that unknowns can be any old thing,
I have 80 + 82 + 94 + 71 plus – you could put in x, you could put in “g” for grade. But you know what? I'm going to
keep the question mark! Look at that! How whimsical! And this will equal, after I divide through by 5, I want that to
equal 85.
Okay, so what do I do? I want to solve for a question mark. Well, first, all of these numbers I can add up and, if you
add 80 and 82, that’s 162. When you add 94 and 71, I think you see 327, and then I have that question mark, dividing
the whole thing by 5. And that equals 85. So I multiply everything through by 5 to clear that 5 denominator, so on this
side it just cancels the 5 and I’m just left with 327 + ? = 5 × 85, which is 425. Well then I subtract the 327 to this side
and what do I see? I see that? = 98. So, in fact, what I see is the student should get exactly a 98 on the last exam,
so that the average overall, five of them, will be an 85. And I would say that is a solid B in my book, but, if there’s a
little grade inflation, there maybe a little “+” there.
Anyway, the answer to the question is the student should get a 98. Not a big deal when you're computing averages.
You just sort of add up all the terms and divide by the total number, not just the four grades, but in fact, this mystery
grade as well, so that it’s equal to 85. You’re all set. Okay, good luck on your test!

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