X + y + z + w = 100

[daftgiraffe]

Hello i need help with this equation.
X + Y + Z + W always equals 100
How do i find Y,Z and W if I increase X by 10 for example.

 

[tkhunny]

Hello i need help with this equation.
X + Y + Z + W always equals 100
How do i find Y,Z and W if I increase X by 10 for example.

Surely there are some additional requirements or descriptions - stating just exactly what it it you want to do?

For Example:
Integer Solutions?
Redistribution rules?

 

[Steven G]

Hello i need help with this equation.
X + Y + Z + W always equals 100
How do i find Y,Z and W if I increase X by 10 for example.

You can't find X, Y, Z or W given what you gave us. Since X is increased by 10, all you can say is that Y+Z+W is now 10 less.

 

[daftgiraffe]

Hi thank you. I have a solution for three components:

• X '+Y '+Z '=100
  
• [FONT=MathJax_Math-italic]Y[FONT=MathJax_Math-italic]Z[FONT=MathJax_Main]=[FONT=MathJax_Math-italic]Y '[FONT=MathJax_Main]′[FONT=MathJax_Math-italic]Z '
  [/FONT][/FONT][/FONT][/FONT]
  [/FONT][/FONT]

[FONT=Georgia, Times New Roman, Times, serif]assuming [/FONT][FONT=MathJax_Math-italic]Z[FONT=MathJax_Main]≠[FONT=MathJax_Main]0[/FONT][/FONT][/FONT][FONT=Georgia, Times New Roman, Times, serif]and X ' is the new fixed value of X

[/FONT][FONT=MathJax_Math-italic]Z[FONT=MathJax_Main]′[FONT=MathJax_Main]=[FONT=MathJax_Main]100[FONT=MathJax_Main]−[FONT=MathJax_Math-italic]X[FONT=MathJax_Main]′[FONT=MathJax_Math-italic]Y[FONT=MathJax_Math-italic]Z[FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]1[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT] and [FONT=MathJax_Math-italic]Y[FONT=MathJax_Main]′[FONT=MathJax_Main]=[FONT=MathJax_Math-italic]Y[FONT=MathJax_Math-italic]Z[FONT=MathJax_Math-italic]Z[FONT=MathJax_Main]′[/FONT][/FONT][/FONT][/FONT][/FONT]

[/FONT][/FONT][FONT=Georgia, Times New Roman, Times, serif]


And I also have a hint of how to go from here, but im pretty bad at math so i havent had any success applying it

[/FONT]Generalization is quite straightforward: Say you have

[FONT=MathJax_Math-italic]kk[/FONT] variables [FONT=MathJax_Math-italic]X[FONT=MathJax_Main]1[FONT=MathJax_Main],[FONT=MathJax_Main]…[FONT=MathJax_Main],[FONT=MathJax_Math-italic]X[FONT=MathJax_Math-italic]k[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]. If you want to assign a new value [FONT=MathJax_Math-italic]X[FONT=MathJax_Main]′[FONT=MathJax_Main]1[/FONT][/FONT][/FONT]to [FONT=MathJax_Math-italic]X[FONT=MathJax_Main]1[/FONT][/FONT]then the system you have to solve is:

[FONT=MathJax_Size2]∑[FONT=MathJax_Math-italic]i[FONT=MathJax_Main]=[FONT=MathJax_Main]1[FONT=MathJax_Math-italic]k[FONT=MathJax_Math-italic]X[FONT=MathJax_Main]′[FONT=MathJax_Math-italic]k[/FONT][/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]100[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]​

and for [FONT=MathJax_Main]1[FONT=MathJax_Main]<[FONT=MathJax_Math-italic]i[FONT=MathJax_AMS]⩽[FONT=MathJax_Math-italic]k[/FONT][/FONT][/FONT][/FONT]
[/FONT]

[FONT=MathJax_Math-italic]X[FONT=MathJax_Math-italic]i[FONT=MathJax_Math-italic]X[FONT=MathJax_Math-italic]i[FONT=MathJax_Main]+[FONT=MathJax_Main]1[FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]X[FONT=MathJax_Main]′[FONT=MathJax_Math-italic]i[/FONT][FONT=MathJax_Math-italic]X[FONT=MathJax_Main]′[FONT=MathJax_Math-italic]i[FONT=MathJax_Main]+[FONT=MathJax_Main]1[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]​

[FONT=Georgia, Times New Roman, Times, serif]

[/FONT][FONT=MathJax_Math-italic]X[/FONT][FONT=MathJax_Main]′[/FONT][FONT=Georgia, Times New Roman, Times, serif]X ''[/FONT]

 

[stapel]

I've fixed the formatting of your post, as much as I could, but questions remain.

Hi thank you. I have a solution for three components:

• X' + Y' + Z' = 100
• YZ = Y"Z'

What do you mean by "a solution", and what do you mean by "three components"? (You've posted two equations in six variables, and no numerical values for any of them.)

assuming that Z ≠ 0, and X' is the new fixed value of X

Does this phrase go with the "solution" part of the post, or with the new stuff (below)?

• Z' = 100 - X'YZ + 1
• Y' = YZZ'

How does this relate to the equations in the "solution" quote above?

Also, I have a hint of how to go from here, but I'm pretty bad at math, so I haven't had any success in applying it.

Generalization is quite straightforward: Say you have k variables X₁, X₂, …, X_k. If you want to assign a new value X′₁ to X₁, then the system you have to solve is:

. . . . .∑i=1kX′k=100

Maybe this is showing up as something sensible on your end, but we're seeing something that makes little sense. Please reply with clarification.

and for 1<i⩽k

. . . . .XiXi+1=X′iX′i+1

Why are the Xi and Xi' repeated? Is there a particular reason for formatting it this way, rather than just using "squared" notation?

X′X ''

This was the last part of your post. What does it mean?

Please be complete. Thank you!