SOLUTION: You have 5 pumpkins, when weighted two at a time these are the weights, 110 112 113 114 115 116 117 118 120 121 pounds. How much does each pumpkin weigh? How do you figure it out?

Question 70198This question is from textbook
: You have 5 pumpkins, when weighted two at a time these are the weights, 110 112 113 114 115 116 117 118 120 121 pounds. How much does each pumpkin weigh? How do you figure it out? What kind of formaula? I've tried formalas but I couldn't figure out the right one, graphing, and tables. I came up with them weighing, 60 61 57 53 and 55 pounds. This question is from textbook

Answer by 303795(602) (Show Source): You can put this solution on YOUR website!
Number the pumpkins from 1 (heaviest) to 5 (lightest)
The two heaviest weigh 121 and the two lightest weigh 110.
Find the average weight of the 5 pumpkins.
=(110 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 120 + 121)/20 = 57.8
Knowing the weights of the two heaviest and two lightest work out the weight of the pumpkin in the middle.
121 + 110 + Pumpkin3 = 5 * (57.8)
231 + Pumpkin3 = 289
ie Pumpkin3 weighs 58 pounds.
The second heaviest weight comes from Pumpkin3 and Pumpkin1.
ie Pumpkin1=120 - 58 = 62 pounds
Pumpkin1 + Pumpkin2 = 121
ie Pumpkin2 = 59 Pounds
The second lightest weight comes from Pumpkin3 and Pumpkin5.
ie Pumpkin5=112 - 58 = 54 pounds
Pumpkin4 + pumpkin5 = 110
ie Pumpkin4 = 56 pounds
So the pumpkin wights are 62, 59, 58, 56 and 54 pounds.
You can easily check if these weights are correct.

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