SOLUTION: Here is the word problem in its exact words. Every year in half moon bay, there is a pumpkin contest to see who has grown the largest pumpkin for that year. Last year, one grower

Question 124945This question is from textbook
: Here is the word problem in its exact words.
Every year in half moon bay, there is a pumpkin contest to see who has grown the largest pumpkin for that year.
Last year, one grower brought 5 pumpkins to the contest. Instead of weighing them one at a time, he informed the judges, "When I weighed them two at a time, I got the following weights: 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 pounds."Find out how much each pumpkin weighed.
I would greatly appreciate it if you could help me with this problem. Thank you. This question is from textbook

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
designate the pumpkins, from lightest to heaviest, with the letters A, B, C, D, E

A+B=110(lightest and 2nd lightest)__ A+C=112(lightest and 3rd lightest)
__ B+C=113(2nd lightest and 3rd lightest)

subtracting 2nd equation from 3rd equation __ B-A=1 __ B=A+1

substituting __ A+A+1=110 __ A=54.5

B=55.5 __ C=57.5

E+D=121(heaviest and 2nd heaviest) __ E+C=120(heaviest and 3rd heaviest)

E=62.5 __ D=58.5
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