Question 714420
"...to obtain 45 gallons of mixture."

Let x and y be the gallons of the 100% concentrate and the 30% strength mixture, respectively, to use.

{{{(1*x+0.3y)/45=0.75}}} AND {{{x+y=45}}}.  Those are a system of simultaneous equations.  Solve for x and y.


The rational equation can be adjusted,
{{{x+0.3y=45*0.75}}}
{{{x+0.3y=33.75}}}, which might be more convenient to use.  Why?


Because the system is equivalently
{{{x+0.3y=33.75}}}
{{{x+y=45}}}
Subtract the first equation from the second equation and very fast solve for y.  Use the value found for y in the second equation to solve for and find the value for x.