Question 720539
An item at a price H was mixed with an item at price L to make M quantity of mixture worth T.  How much of each item was used?


Let u = amount of lower priced item to use
Let v = amount of higher proced item to use


{{{highlight((Lu+Hv)/M=T)}}} and {{{highlight(u+v=M)}}}.  Solve for and find u and v.


From rational equation, {{{Lu+Hv=TM}}}.  Using the M sum equation, {{{v=M-u}}}.
{{{Lu+H(M-u)=TM}}}
{{{Lu+HM-Hu=TM}}}
{{{Lu-Hu=TM-HM}}}
{{{(L-H)u=(T-H)M}}}
{{{u=(T-H)M/(L-H)}}}, and because T-H and L-H are both negative, multiplication by {{{(-1)/(-1)}}} gives us:
{{{highlight(u=(H-T)M/(H-L))}}}.


You can continue onward to solve for v, and then substitute given values to compute u and v.