Question 730719
M liters of an T% alcohol solution is obtained by mixing a H% solution with L% solution. How many liters as u and v of each solution must be used to obtain the desired mixture?


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


You could begin with transforming the rational equation.
{{{Lu+Hv=TM}}}, and try solving for one of the variables in the M equation and substitute into the transformed rational equation, as an example,
{{{v=M-u}}},
then
{{{Lu+H(M-u)=TM}}}
{{{Lu+HM-Hu=TM}}}
{{{Lu-Hu+HM=TM}}}
.
which allows you to obtain a formula for u.
.
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