Pow 1 Haybaler Problem

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Haybaler Problem
Problem Statement: We are trying to find the weight of 5 hay bales. The bales of hay were weighed in pairs. The weights of the pairs in kilograms were 80,82,83, 84,85,86,87,88,90, and 91. What are the weights of the individual bales? Is there an easier way to find the weights? Process: What our group is doing is the guess and check method. We did this because we thought that would be the best and easy way. Also , we labeled the hay bales A,B,C,D,E because that makes it easier to keep track of all our numbers . When we did the guess and check part , it was frustrating . I say this because you can have all the numbers you need but that one number , and just missing the one number can change the entire order that you already have. To try to fix this problem , instead of everyone doing the same thing , two of us would try a different set of numbers while the other two try another set of numbers . Then , afterwards we would check our answers every now and then . We also tried to give each of us a different number (ex: 43,44,47,38 ) , to work on and check if it works..we thought this would be another faster way of finding the answer . (I didn’t find the solution on my own but I figured the answer out with my groups .)
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So we decided to start with the number 80 and went down the order . We find out that the correct answers are 39,41,43,44, and 47. What we did first was A+B= 80. A=39,B=41,C=43,D=44 , and E=47,so A+B = 39+41. So , after that we continued to do A+C ( 39+43=82), A+D (39+44=83) , and A+E (39+47=86) . Next , we switched the first variable to B , now it is B+C (41+43=84), B+D (41+44=85), and B+E (41+47=88) . We continued to do that C+D (43+44=87) ,C+E(43+47=90). Then the last combination is D+E (44+47=91) . We never proved there were any other answers , but we checked a lot of different numbers. So, the answers 39,41,43,44,41 are the correct

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