SOLUTION: Question: Suppose five bales of hay are weighed two 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 ea

Question 329544: Question: Suppose five bales of hay are weighed two 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 bale weigh?
Is this an average question? I don't think that it is but I can't figure how to set this up.
Thank you
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
from lightest to heaviest , let the bales be a , b , c , d , and e

a + c = 112 ___ a = 112 - c

the two lightest ___ a + b = 110 ___ b = 110 - a = c - 2

c + e = 120 ___ e = 120 - c

the two heaviest ___ d + e = 121 ___ d = 121 - e = c + 1

each bale is weighed twice ___ a + b + c + d + e = (110 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 120 + 121) / 2

substitute to find c , then substitute back to find the others
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