Question 824856
Two-Part Mixture problem.  Let us see what we can do.


Assigning Variables,
L = 2% G
T = 5% G
H = 10% G
z = Amount of mixture in tons
x = amount of the H material
y = amount of the L material


You have six variables, and THREE of them are UNKNOWN.  If you wish to solve the problem specifically, you would need to be able to find THREE equations!  Right now, x, y, and z are unknown.


You are only able to obtain these equations:
{{{(Ly+Hx)/z=T}}} and {{{x+y=z}}}


You are then GIVEN a value for y and if y=10, then you CAN FIND x and z.


You are later given a value for z and if z=16, then you can find values for y and x.


If you are given BOTH x and y, then you only need the simple equation x+y=z to get a value for x.  


For just (1) alone, then the unknowns are x and z.
{{{y=z-x}}}.  Substitute.
{{{L(z-x)+Hx=Tz}}}
{{{Lz-Lx+Hx=Tz}}}
{{{Lz-Tz=Lx-Hx}}}
{{{z(L-T)=x(L-H)}}}
{{{z=x(L-H)/(L-T)}}}.
Reuse the simple equation {{{x+y=z}}};
{{{x+y=x(L-H)/(L-T)}}}
{{{y=x(L-H)/(L-T)-x}}}
{{{y=x((L-H)/(L-T)-1)}}}
{{{x=y/((L-H)/(L-T)-1)}}}
{{{x=y((L-H)/(L-T)-(L-T)/(L-T))}}}
{{{x=y(L-T)/((L-H)-(L-T))}}}
{{{highlight(x=y(L-T)/(T-H))}}}, again, keeping in mind right now x is the solved variable and y is a known variable.
Solve similarly for z.