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### Increasing the Average

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Date: 02/25/2001 at 16:02:25
From: Hunter Darbonne
Subject: Help PLease (averages)

Five members of a basketball team are weighed and an average weight is
recalculated after each member is weighed. If the average increases
two pounds each time, how much heavier is the last player than the
first?

I worked at it and did not get the answer right, so my teacher gave me
a hint. She said to try picking a weight for the first person, for
example 160, and then see how much the next person has to weigh in
order for the average to increase. I am still puzzled and need help.

Hunter
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Date: 02/25/2001 at 22:46:35
From: Doctor Peterson
Subject: Re: Help PLease (averages)

Hi, Hunter.

Let's follow your teacher's suggestion. Suppose the first player
weighs 160 pounds, and the average of the first two is two pounds
more, or 162 pounds. What is the second player's weight? Well, to find
the average, we had to add the two weights and divide by 2. So the sum
of the two weights has to be 324 (twice 162), and the second player
must weigh 324-160 = 164 pounds.

You can continue the same thinking to find what each of the five has
to weigh. Then you'll want to convince yourself that the result
doesn't depend on the choice of 160 to start with. Think about the
reasoning you used, and you should be able to see why it doesn't.

If you happen to know a little algebra, you can write an equation for
each step. Here's what I did above, algebraically:

(X + Y)/2 = X + 2

X + Y = 2X + 4

Y = X + 4

This shows that the second player must weigh 4 pounds more than the
first, no matter what "X" is! You can do the same three more times,
with different numbers of players.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Basic Algebra
Middle School Algebra
Middle School Word Problems

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