Question 741162
Is that beaker big enough?


Let y = gallons of 70% alcohol to add.


{{{(3*40+y*70)/(totalVolumeOfMixture)=61}}}

That is the 61% target concentration is the ratio of total amount of alcohol to the total amount of solution, expressing concentrations as percents.


{{{highlight((3*40+y*70)/(3+y)=61)}}}
Solve for y.


You could do it like, {{{(3*0.40+y*0.70)/(3+y)=0.61}}} but you may still multiply both sides by 100, so you'll have the equivalent of the above highlighted equation.


Further steps,
{{{40*3+70y=61(3+y)}}}
{{{40*3+70y=3*61+61*y}}}
{{{40*3+70y-61y=3*61}}}
{{{40*3+9y=3*61}}}
{{{9y=3*61-3*40=3(61-40)}}}
{{{9y=3*21}}}
{{{y=3*3*7/9}}}
{{{highlight(y=7)}}}