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/
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