Question 119685
x = number of gallons of 30% alcohol solution
y = number of gallons of 60% alcohol solution
In words:
(alcohol contained in x + alcohol contained in y) / 18 = 50%
{{{(.3x + .6y) / 18 = .5}}}
and, of course,
{{{x + y = 18}}}
In the 1st eqaution,
{{{.3x + .6y = 9}}}
divide both sides by {{{.3}}}
{{{x + 2y = 30}}}
{{{x + y = 18}}}
Now subtract the bottom equation from the top
{{{y = 12}}}
{{{x + y = 18}}}
{{{x = 6}}}
6 gallons of the 30% solution must be mixed
with 12 gallons of the 60% solution
check answer:
{{{(.3x + .6y) / 18 = .5}}}
{{{(.3*6 + .6*12) / 18 = .5}}}
{{{(1.8 + 7.2) / 18 = .5}}}
{{{9/18 = .5}}}
{{{.5 = .5}}}
OK