SOLUTION: 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,

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
RELATED QUESTIONS
Question: Suppose five bales of hay are weighed two at a time in all possible ways. The... (answered by scott8148)

supose 5 bales of hay are weighed 2 at a time in all possible ways. the weights in pounds (answered by khwang)

suppose five bales of hay are weighed two at a time in all possible ways. the weights in... (answered by khwang)

farmer ted goes to the auction each week and buys lots of hay bales. last week he bought... (answered by Boreal)

A farmer orders 3 3/4 bales of hay. He spreads 2/5 of the delivery around the stables and (answered by rfer)

There are 42 bales of hay in the barn. Tom stacked more bales in the barn today.... (answered by swincher4391)

Out of 2 million hay fever sufferers, 20% are allergic to tree pollen. If 11 hay fever... (answered by edjones)

there are 5 sacks, and they are weighed 2 at a time. Their weights are... (answered by ikleyn,M15T4K3)

I don not understand this question at all! 1.Suppose you are an event coordinator for a... (answered by ewatrrr)