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?

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.

Ahh. Simple algebra :) Thanks so much.