Question

Suppose five pumpkins are weighed two at a time in all possible ways. The weights in pounds are recorded as 16,18,19,20,21,22,23,24,26, and 27. How much does each individual pumpkin weigh?

Answer 1

$a+b=16 => \boxed{a=16-b} \\ \\ b+c=18=>\boxed{c=18-b} \\ \\c+d=19 \\ \\ a+c=21 \\ \\ d+e=20 \\ \\ a+d=22 \\ \\ a+e=23 \\ \\ b+d=24 \\ \\ b+e=26 \\ \\ \\ a+c=21 \\ 16-b+18-b=21 \\ 32-2b=21 \\ -2b=21-34 \\ -2b=-13 \\ \\ \boxed{b=\frac{-13}{-2}=6.5} \\ \\ a=16-6.5 \\ \\ \boxed{a=9.5} \\ \\ c=18-6.5 \\ \\ \boxed{c=11.5} \\ \\ d=19-11.5 \\ \\ \boxed{d=7.5} \\ \\ e=20-7.5 \\ \\ \boxed{e=12.5}$