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Math Help - an interesting word problem.

  1. #1
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    an interesting word problem.

    I was doing this word problem for fun (a conundrum of sorts on a game) and I just cannot figure it out! I'm sure the answer is simple but I feel like I'm missing a step somewhere. This is the word problem:

    5 Puppies were weighed on a scale. However, they were weighed two at a time, ten times total , so that every possible combination of two puppies was weighed. The scale had the following readouts for the pairs: 236 pounds, 244 pounds, 228 pounds, 250 pounds, 258 pounds, 230 pounds, 246 pounds, 238 pounds, 242 pounds, and 252 pounds.

    How heavy was the heaviest puppy?
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  2. #2
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    Let the weights of the puppies be, in order, A,B,C,D,E. Then the largest value of the ten is A+B=258 and the smallest is D+E=228. The sum of all ten values is 4(A+B+C+D+E)=2424, so A+B+C+D+E=606 and hence C=120.

    Now the second largest value is 252 and this is A+C, so that A=132 and B=126. Similarly D=118 and E=110.

    The answer is 132.
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  3. #3
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    Ahh. Simple algebra Thanks so much.
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