Question 784649
ASSIGN VARIABLES TO ALL QUANTITIES
L, the lower concentration of available material, 45%
H, the higher concentration of available material, 55%
T, the target concentration of resulting mixture, 50%
M, the amount of resulting mixture, 600 ml.
x, the amount of lower concentrated material to use, unknown 
y, the amount of higher concentrated material to use, unknown


EQUATION 

{{{highlight((Lx+yH)/M=T)}}} and {{{highlight(x+y=M)}}}

{{{(Lx+yH)/M=T}}}
{{{Lx+yH=TM}}}
{{{Lx+(M-x)H=TM}}}
{{{Lx+HM-Hx=TM}}}
{{{(L-H)x+HM=TM}}}
{{{(L-H)x=TM-HM}}}
{{{(L-H)x=(T-H)M}}}
{{{x=M(T-H)/(L-H)}}}, and since the two differences here would both be negative, 
we can multiply by (-1)/(-1),
{{{highlight(x=M(H-T)/(H-L))}}}


After using that formula, you can simply use {{{highlight(y=M-x)}}}


Substitute the necessary values and compute x and y.