Question 784974
ASSIGN VARIABLES
H = 70%
L = 20%
T = 40%, concentration wanted
M = 50 quarts, quantity wanted
u = unknown volume of 20%
v = unknown volume of 70%



MAKE EQUATIONS FOR SYSTEM


{{{highlight((Lu+Hv)/M=T)}}} and {{{highlight(u+v=M)}}}


Solve for u and v.  The equations will be linear so the rational one with T is easily transformed into a more familiar format.


{{{v=M-u}}}, and {{{Lu+Hv=TM,}}}
{{{Lu+H(M-u)=TM}}}
{{{Lu-Hu+HM=TM}}}
{{{(L-H)u=TM-HM}}}
{{{u=(TM-HM)/(L-H)}}}
{{{u=M(T-H)/(L-H)}}}
Divide by or multiply by {{{(-1)/(-1)}}} because computations will be easier that way:
{{{highlight(u=M(H-T)/(H-L))}}}
'
Use that for u and then go back to {{{highlight(v=M-u)}}}.


SUBSTITUTE THE GIVEN VALUES TO FIND THE UNKNOWN VALUES

Just use the number values from the description, listed as "ASSIGN VARIABLES".