SOLUTION: 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 we

Question 22826: 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
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
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
Let them be A,B,C,D & E. (in increasing order)
Since each of them appeared in the list of partial sums 4 times(why ?)
we have 4(A+B+C+D+E)= 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 = 1156.
So, A+B+C+D+E = 289.
We see that A+B = 110 & D+E = 121, so C = 289-(110+121) = 58.
Also, since A+C = 112, we get A = 112-58= 54,B = 110 - 54 = 56.
Similarly, C+E = 120, E = 120 - 58 = 62, D = 121 - 62 = 59.
Answer: 54, 56, 58, 59, 62.

Kenny

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