Is it possible to solve for any variable in this system of equations? (All variables must be > 0; no variable can be +- 10,000 from another)

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DatMathGuy

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All variables must be greater than 0 and no variable can be +- 10,000 from another.
158,255= x + y + z
156,639= y + z + a
157,982= z + a + b

Is it possible to solve for any variable in this system of equations?
 
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DatMathGuy said:
All variables must be greater than 0 and no variable can be +- 10,000 from another.
158,255= x + y + z
156,639= y + z + a
157,982= z + a + b

Is it possible to solve for any variable in this system of equations?
Click to expand...

You have three equations in six unknowns. Kinda by definition, you cannot solve for unique numerical values.
 
DatMathGuy said:
All variables must be greater than 0 and no variable can be +- 10,000 from another.
158,255= x + y + z
156,639= y + z + a
157,982= z + a + b

Is it possible to solve for any variable in this system of equations?
Click to expand...
First, what does "no variable can be +- 10,000 from another" mean? Is it that no difference between variables can be exactly 10,000, or at least that, or at most that?

Second, are you also requiring the variables to be whole numbers?

Third, does "solve for any variable" mean "find at least one set of values that satisfy the conditions", or "solve for any one variable in terms of the others", or "find a unique set of values", or something else?

The fact is that there are many solutions.
 
Appreciate your help, I was really looking for possible solutions. I wonder if I can make a formula which shows a range if possible solutions with the give criteria. Btw I was trying to say none of the variables could be more than 10000 apart so I couldn't use 55000 for x and 30000 for b. Here is what i came up with:

X = 54005
Y = 52750
Z = 51500
A = 52389
B = 54093
 
DatMathGuy said:
Appreciate your help, I was really looking for possible solutions. I wonder if I can make a formula which shows a range if possible solutions with the give criteria. Btw I was trying to say none of the variables could be more than 10000 apart so I couldn't use 55000 for x and 30000 for b. Here is what i came up with:

X = 54005
Y = 52750
Z = 51500
A = 52389
B = 54093
Click to expand...
Welcome to the forum.
Now you need to show that these values work in each equation.
It really isn't nice that you would want anyone here to check your work. So, please check it yourself and post back with your results. Of course, if you are having trouble checking your results then please ask for help.
 
Thank you for your warm welcome. I never asked anyone to check my work. I provided one of several solutions to the problem I proposed. I then asked if it is possible to derive a formula to provide a range of values that would solve for the variables given the constraints I’ve outlined. Any assistance would be greatly appreciated.
 
Can we see how you got your answer? Usually, the method used to get your result (assuming that it is correct) would also show that there are other solutions since (as already pointed out) you have more variables than equations.
What topic did this problem come from? That would greatly help us determine how you can find other solutions (or to show that there are no solutions)
 
DatMathGuy said:
Appreciate your help, I was really looking for possible solutions. I wonder if I can make a formula which shows a range if possible solutions with the give criteria. Btw I was trying to say none of the variables could be more than 10000 apart so I couldn't use 55000 for x and 30000 for b. Here is what i came up with:

X = 54005
Y = 52750
Z = 51500
A = 52389
B = 54093
Click to expand...
Thanks for the clarification. But it still isn't clear exactly what you are asking for. Does "a range of possible solutions" mean a formula that generates all solutions? (It would probably be more a procedure than a formula.)

It will help a lot if you can show how you got these (which I haven't checked yet), as that would show us what methods you know, and might be modifiable to produce the sort of answer you want.
 
I stumbled upon this problem on my own but I’m sure it has been answered many times. I found my solution essentially through trial and error.

The solution I originally provided is the following (it is correct):

X -> 54005
Y -> 52750
Z -> 51500
A -> 52389
B -> 54093

158255 = X + Y + Z
156639 = Y + Z + A
157982 = Z + A + B

The above formula are also satisfied with the give variables:

X -> 54004
Y -> 52751
Z -> 51500
A -> 52388
B -> 54094

I’m wondering if there is a way to determine a range of possible solutions for each of these variables given the constraints.
 
I have never seen a problem with a constraint that says that no two values can be greater than some given amount. That doesn't really matter.
What would happen if you add say 50 to x, y, a and b subtract 100 from z OR add 200 to x, y, a and b subtract 400 from z??
 
Steven G said:
I have never seen a problem with a constraint that says that no two values can be greater than some given amount. That doesn't really matter.
What would happen if you add say 50 to x, y, a and b subtract 100 from z OR add 200 to x, y, a and b subtract 400 from z??
Click to expand...
Maybe I wasn't clear, the constraint says that none of the variables can have an absolute difference greater than 10,000. Yes, the solutions you provide do satisfy the formula but say you were to add 5000 to x, y, a, and b and subtract 10,000 from z. This would satisfy the formula as well but
|x-z}>10,000:
x = 59004
y = 57751
z = 41500
a = 57388
b = 59094

Would it be possible to determine ranges of solutions for these variables?
 
It seems possible to find a range. I do understand the constraint that you mentioned and that is why I put relatively small number to add and subtract from the solution which you mentioned. Give it a try to see what numbers can be added and subtracted from the variables you already found yet stay within the constraint that no TWO variables can differ by more than 10,000.
 
DatMathGuy said:
I stumbled upon this problem on my own but I’m sure it has been answered many times.
Click to expand...
Do you mean that you found the problem somewhere, or that it came up in the course of some project, or that you made up the problem for no particular reason?

It's worth knowing that it's very easy to make up a problem that is very hard, or even impossible, to solve; and if a problem has no context that justifies an effort, then it likely will not be worth anyone's time to try to solve it.

If there were a contextual reason for the problem, rather than random curiosity, then that might suggest what sort of answer is really needed. Possibly your "range of possible solutions for each of these variables" just means to find the lowest and highest possible value of each, but that doesn't seem particularly useful.
 
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