1. A certain farmer was weighing his five hay bales before he stored them in the barn. For some strange reason, he weighed them in all the possible pairs of two bails and only wrote down the total weight for each pair. He also didn’t keep track of what two bales made up the weight. The weights he got were 80, 82, 83, 84, 85, 86, 87, 88, 90, and 91. Your job is to figure out the weights of the five hay bales, and if there is more than one set of weights.

2. In attempting to solve this problem, I first tried a bunch of guess and check. After about 45 minutes of getting nowhere, I worked on finding the smallest number. First, I drew 5 hay bales to get a visual representation.

Once I had that, I decided that bale 1 was the lightest and bale 5 was the heaviest and the other bales are progressively heavier from 1-5. This told me that the two bales that weighed 91 pounds together would be bales 4 and 5 (the two heaviest bales), and the two bales that weighed 80 pounds together would be bales 1 and 2 (the two lightest bales). So with this information, I tried to find out the weight of bale 1 by itself. First I made a chart to find the different bale pairs there were (without repeating) to make up the nine two-bale sums. |1+2 |2+3 |3+4 |4+5 |1+3 |2+4 |3+5 |- |1+4 |2+5 |- |- |1+5 |- |- |-

Then I tried having bale 1 being 40 pounds, but that would mean that bale 2 was also 40 pounds, and having two bales of the same weight would mean that there were two bale-pairs that came out to the same amount, and that wasn’t the case, so bale 1 had to have a different weight than bale 2. so, by using guess...

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