Increasing the Average

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. 
Could someone please help me?

Hunter

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/