Question 178369
If I understand the setup of this problem correctly...then the answers(weight of each pumkin) are  rational numbers not integers.
:
let a,b,c,d,e be the weights of each pumpkin
:
answers:
:
a=13/2
b=19/2
c=23/2
d=25/2
e=29/2
:
to get the value of a:
:
a+b=16....eq 1
a+c=18....eq 2
:
c=21-b.....substitute that value into eq 2
:
a+b=16....eq 1
a+(21-b)=18..eq 2 revised
:
now add the two equations together
:
2a=13
:
a=13/2
:
with a as an answer you just need to substitute that into the remaining the appropriate equation to find b and just keep following that pattern to find each value.
:
a+b=16
a+c=18
a+d=19
a+e=20
b+c=21
b+d=22
b+e=23
c+d=24
c+e=26
d+e=27