Answer
2 units of mix A, 3 units of mix B, 1 unit of mix C
Work Step by Step
A: $4x+6y+4z=30$
B: $6x+y+z=16$
C: $3x+2y+12z=24$
3A-C
$3*(4x+6y+4z)-(3x+2y+12z)=3*30-24$
$12x+18y+12z-3x-2y-12z=90-24$
$9x+16y=66$
12B-C
$12*(6x+y+z)-(3x+2y+12z)=16*12-24$
$72x+12y+12z-3x-2y-12z=192-24$
$69x+10y=168$
$9x+16y=66$
$69x+10y=168$
$5*(9x+16y)-8*(69x+10y)=66*5-8*168$
$45x+80y-552x-80y=330-1344$
$-507x=-1014$
$-507x/-507=-1014/-507$
$x=2$
$9x+16y=66$
$9*2+16y=66$
$18+16y=66$
$16y=48$
$16y/16=48/16$
$y=3$
$6x+y+z=16$
$6*2+3+z=16$
$12+3+z=16$
$15+z=16$
$z=1$
