Can you solve for six variables given their weighted sum equals 100?

[mirmidonas55]

First of all excuse my English.



I have the following problem and I don't know if it can be solved.



We have the following equations:



A*X1=B*X2=C*X3=D*X4=E*X5=F*X6 and

X1+X2+X3+X4+X5+X6=100



If we know the values of A,B,C,D,E,F can we found the values of X1,X2,X3,X4,X5,X6?



Can anyone help me?
Sorry if I didn't make the post in the correct category

 

[danago]

Yep it can be done.

The way that i would solve it would be to form the six equations:

AX₁ = c
BX₂ = c
:
FX₆ = c

Where c is some fixed constant. Can you see how i can form these equations?

You can then easily use these separate equations along with the last equation (X1+X2+X3+X4+X5+X6=100) to find what the constant c is, and hence what each X is.

 

[mirmidonas55]

Thank you danago