When Uranium is enriched, what proportion of it becomes enriched U and what proportion becomes depleted U?

let x = mass of source Uranium,
y = mass of depleted Uranium,
z = mass of enriched Uranium,
p = depleted mass as a proportion of source mass (i.e. p = y/x),
q = enriched mass as a proportion of source mass (i.e. q = z/x),
s = proportion of ²³⁵U in the source Uranium by mass,
d = proportion of ²³⁵U in depleted Uranium by mass and
e = proportion of ²³⁵U in enriched Uranium by mass. 

x = y + z (U mass before = U mass after)
sx = dy + ez ( mass of ²³⁵U before = mass of ²³⁵U after)
=> y = x - z (from U mass equation)
substitute into ²³⁵U mass equation:
sx = d(x - z) +ez
solve for z:
z = x (d - s)/(d - e)
thus:
q = z/x = (d - s)/(d - e)
similarly:
p = (e - s)/(e - d)

Answer:
p = (e - s)/(e - d)
q = (d - s)/(d - e) 

Typical values:
proportion of ²³⁵U in the source Uranium by mass, s = 0.71% = 0.0071
proportion of ²³⁵U in depleted Uranium by mass and, d = 0.2% = 0.002
proportion of ²³⁵U in enriched Uranium by mass, e = 3.5% = 0.035

p = (0.035 - 0.0071)/(0.035 - 0.002)
= 0.845
= 84.5%

q = (0.002 - 0.0071)/(0.002 - 0.035)
= 0.155
= 15.5%

Thus 1272 tonnes of source Uranium becomes 1075 tonnes (= 1272 x 84.5%) of depleted Uranium and 197 tonnes (= 1272 x 15.5%) of enriched Uranium.

Copyright (c) 2000, Paul Dyson. May be reproduced with acknowledgement of the author.