Question 145804: This is a verbal question that has to do with Quadratic Equations.
Suppose 5 bales of hay are weighed 2 at a time in all possible ways. The weights in pounds are 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121. How much does each of the 5 bales weigh?
I'd appreciate any help with this problem. Thanks.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! call the bales (in order of increasing weight) A, B, C, D, E
the lowest and highest weights are the 2 lightest and 2 heaviest respectively
__ A+B=110 __ D+E=121
the 2nd lowest is the lightest bale with the middle bale __ A+C=112
the 2nd highest is the heaviest bale with the middle bale __ C+E=120
every bale is weighed with each of the other 4 bales, so every bale is weighed 4 times
__ this means that the sum of the weights is 4 times the sum of the weights of the individual bales
A+B+C+D+E=(110+112+113+114+115+116+117+118+120+121)/4 __ A+B+C+D+E=289
substituting __ 110+C+121=289 __ C=58
substituting __ A+58=112 __ A=54
substituting __ 54+B=110 __ B=56
substituting __ 58+E=120 __ E=62
substituting __ D+62=121 __ D=59
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