If Sandra mixes <em>x</em> L of 65% solution with <em>y</em> L of 90% solution, then the resulting mixture has a total volume of
<em>x</em> + <em>y</em> = 500
litres, and it contains
0.65<em>x</em> + 0.90<em>y</em> = 0.75 (500) = 375
litres of alcohol.
Solve the first equation for <em>y</em> :
<em>y</em> = 500 - <em>x</em>
<em />
Substitute this into the second equation and solve for <em>x</em> :
0.65<em>x</em> + 0.90 (500 - <em>x</em>) = 375
0.65<em>x</em> + 450 - 0.90<em>x</em> = 375
75 = 0.25<em>x</em>
<em>x</em> = 300
Solve for <em>y</em> :
<em>y</em> = 500 - 300
<em>y</em> = 200
So, Sandra should mix 300 L of 65% solution with 200 L of 90% solution.
Using a graphical tool we obtain that the solution of this system
(intersection between the lines)
is given by the point
(x,y) = (2,4)
