by Bill Graham

At first, it seems there’s not enough information. I’m sure you wanted to know the number of players on the team. But, it turns out that the problem can be solved without that information.

I can think of three ways of solving this: guess and check, algebra or a sideways approach. Here’s the sideways approach.

If Humphrey weighs 22 pounds more than the team average and he increases the average by one pound, then you had to divide by 22 when he joined the team, or the original team must have had 21 players.

If the original total weight divided by 21 equals 177, the original total weight must be 3,717 pounds. Then Humphrey adds 199 pounds to the total, divided by 22 players equals the new average of 178.

To finish the problem, the new total including Humphrey is 3,916 pounds plus the weight of Humphrey’s sister divided by 23 must equal 179.

In case you don't like the sideways approach, here's the algebra approach.
Let W = team average weight (177). Let H = Humphrey's weight (199).
Let S = weight of Humphrey's sister (unknown).
Let N = number of players on team before Humphrey joined (unknown).
Let W_H = team average weight with Humphrey on it (178).
Let W_S = team average weight with Humphrey and sister on it (179).
NW = total weight before Humphrey.

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Contents copyright 2005 by Bill Graham and ParaComp, Inc. All rights reserved.
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