Question 759061
This extremely common two-part mixture problem can be handled with two equations: One is a rational equation using two unknown variables and another is a simple sum linear equation using the same two unknown variables.


ASSIGN VARIABLES TO ALL QUANTITIES
H = concentration, such as percent, of the high concentration material
L = concentration such as percent, of the low concentration material
T = the target concentration desired for the mixture
M =  amount of mixture at the target concentration
u = amount of low concentration material to use (unknown)
v = amount of high concentration material to use (unknown)


ACCOUNT FOR PURE COMPONENT
{{{u*L+v*H}}} is the amount of pure component
The concentration is then in the quantity of mixture, M,
{{{(uL+vH)/M}}} is the resulting percent concentration for this example.


ACCOUNT FOR  MATERIAL AMOUNTS
Simply {{{M=u+v}}}


EQUATIONS TO FORM THE SYSTEM
{{{highlight((Lu+Hv)/M=T)}}} and {{{highlight(u+v=M)}}}


Solve the system for u and v.
Substitute the given known values to find the resulting values for u and v.