Question 713915
The manufacturer wants to mix some high strength cheese with so low strength cheese and have a known quantity of mixture of a known intermediate strength cheese.  Strength here is money, price (some expected dollars per pound).


M=pounds of mixture, 30 pounds.
u= amount of low strength, unknown pounds
v= amount of high strength cheese, unknown pounds
L = strength of the low strength cheese, $4/pound
H = high strength cheese, $7/pound
T = Target price per pound 5.70



Setup Equations.
{{{(Lu+Hv)/M=T}}}
{{{u+v=M}}}



Solve for u and v.
Sometimes the values given are conveniently chosen to make the solving easy, but you don't want to always rely on that.
{{{Lu+Hv=TM}}}
and
{{{u+v=M}}}
How neat those numbers will be, we not know (unless we substitute them NOW).
v=M-u, so keep going in symbols, subsituting this one into the percents equation:
{{{Lu+H(M-u)=TM}}}
{{{Lu+HM-Hu=TM}}}
{{{(L-H)u+HM=TM}}}
{{{(L-H)u=TM-HM}}}
{{{(L-H)u=M(T-H)}}}
{{{u=M(T-H)/(L-H)}}}


Might be most convenient if done symbolically to use 
{{{highlight(u=M(H-T)/(H-L))}}}, which was multiplied by {{{(-1)/(-1)}}}
and
{{{highlight(v=M-u)}}}, since you just found u.



Substitute Values to determine values of u and v.
{{{u=(M(7-5.7))/(7-4)}}}, which you compute and then find the value for v.