How to derive a value.

[tendemo]

X + Y = Z
How can I obtain a value for X so that at any given time, X = .3 of Z or in other words 3% of Z, whereby Y is always a fixed value ?

[techgnome]

if X is 3% of Z, then Y must also be 97% of Z.... And at the same time, X = Z - Y ... So if Y is constant, so will X and Z. - If any one of them changes, so do the other two, to maintain the proper ratio.
Possible values for X, Y, Z that seem to work:
3, 97, 100
and their respective multiples - which must be applied across the entire set.

-tg

[jemidiah]

X is a function of Z, which is a function of t (apparently). Y is not a function of t. We have

X(Z(t))+Y=Z(t).

We also know that for any t, X = 0.03 of Z (I presume you truly meant 3% and not 30%), or X(Z(t))=0.03Z(t). Throwing this in to the above, we get

0.03Z(t) + Y = Z(t)

implying

Y = (0.97)*Z(t).

So... y isn't a constant as time evolves, unless Z happens to be. Proceeding under the assumption that Z(t) = c for some constant c, X(Z(t)) = X(c) = 0.03c = a constant.

To answer the original question, "How can I obtain a value for X so that at any given time, X = .3 of Z or in other words 3% of Z, whereby Y is always a fixed value ?", you fix Z to be a constant (100 in techgnome's example), which forces X to be a constant (3 above), which then forces Y to always be a fixed value (97 above).

I went through the time derivation to show that time falls out of this problem as you've asked it. Maybe something's wrong in the problem statement, though, since you seem to think time is important for this problem.

[tendemo]

Logical approach, I actually meant .3 or 30% sorry about the mislead. Now what will be Y and Z if X = 30 following your approach. Thanks

[techgnome]

70 & 100 respectively. It's still the same logic as before.

-tg