SOLUTION: Five pumpkins are weighed two at a time in all ten sets of two. The weights are recorded as 16, 18,19, 20, 21, 22, 23, 24, 26, and 27 pounds. All individual weights are also intger

Algebra ->  Formulas -> SOLUTION: Five pumpkins are weighed two at a time in all ten sets of two. The weights are recorded as 16, 18,19, 20, 21, 22, 23, 24, 26, and 27 pounds. All individual weights are also intger      Log On


   

Question 178369: Five pumpkins are weighed two at a time in all ten sets of two. The weights are recorded as 16, 18,19, 20, 21, 22, 23, 24, 26, and 27 pounds. All individual weights are also intgers. How much does each pumpkin weigh?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
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