Answer
120 liters of 25% concentrate, 60 liters of 40% concentrate, 20 liters of 50% concentrate
Work Step by Step
25%, 40%, 50% concentrates
want 200 liters of 32%
$x$, $y$, $z$ are respectively the amounts of the 25%, 40%, and 50% concentrates
$.25x+.4y+.5z=200*.32$
$x+y+z=200$
$x=2y$
$x+y+z=200$
$x=2y$
$2y+y+z=200$
$3y+z=200$
$.25x+.4y+.5z=200*.32$
$.25x+.4y+.5z=64$
$4*(.25x+.4y+.5z=64)$
$x+1.6y+2z=256$
$x=2y$
$x+1.6y+2z=256$
$2y+1.6y+2z=256$
$3.6y+2z=256$
$3.6y+2z-3.6y=256-3.6y$
$2z=256-3.6y$
$3y+z=200$
$2*(3y+z=200)$
$6y+2z=400$
$6y+2z-6y=400-6y$
$2z=400-6y$
$256-3.6y=400-6y$
$256-3.6y+6y-256=400-6y+6y-256$
$2.4y=144$
$2.4y/2.4=144/2.4$
$y=60$
$x=2y$
$x=2*60$
$x=120$
$x+y+z=200$
$120+60+z=200$
$180+z=200$
$180+z-180=200-180$
$z=20$
