If Sandra mixes x L of 65% solution with y L of 90% solution, then the resulting mixture has a total volume of
x + y = 500
litres, and it contains
0.65x + 0.90y = 0.75 (500) = 375
litres of alcohol.
Solve the first equation for y :
y = 500 - x
Substitute this into the second equation and solve for x :
0.65x + 0.90 (500 - x) = 375
0.65x + 450 - 0.90x = 375
75 = 0.25x
x = 300
Solve for y :
y = 500 - 300
y = 200
So, Sandra should mix 300 L of 65% solution with 200 L of 90% solution.
