# an interesting word problem.

• Apr 1st 2006, 06:05 AM
irkenequine
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?
• Apr 1st 2006, 12:10 PM
rgep
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.