Question 754290
How many ounces,u of a nameOfMetal alloy that costs $L per ounce should be mixed with v ounces that costs $H per ounce to make a new M ounce alloy that costs $T per ounce? 


This is the same general mixture problem like so many others of the same form.


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

Solve this system for u and v.

{{{Lu+Hv=TM}}} and from the material balance v=M-u so substitute.
{{{Lu+H(M-u)=TM}}}
{{{Lu+HM-Hu=TM}}}
{{{Lu-Hu=TM-HM}}}
Multiply both sides by negative 1.
{{{Hu-Lu=HM-TM}}}
{{{u(H-L)=(H-T)/M}}}
{{{highlight(u=M(H-T)/(H-L))}}}


and continuation to solve for v will use similar skills.