Question 203003

We need 54 liters 

Let x=amount of commercial spray X needed
y=amount of commercial spray Y needed
z=amount of commercial spray Z needed

x+y+z=54 -------------eq1
(1/5)x+(1/2)z=12--------eq2
(2/5)x+(1/2)z=16--------eq3
(2/5)x+y=26----------------eq4

eq3-eq2:
(1/5)x=4
x=20 liters------amount of commercial spray X needed
Substitute into eq4:
(2/5)*20+y=26
8+y=26
y=26-8=18 liters----------------amount of commercial spray Y needed
From eq1
20+18+z=54
z=16 liters ----amount of commercial spray Z needed

CK
CHEMICAL A:  (1/5)*20+0+((1/2)*16=4+8=12 liters----CK
CHEMICAL B:  (2/5)*20+0+(1/2)*16=8+8=16 liters-----CK
CHEMICAL C:  (2/5)*20+18+0=8+18=26 liters----------CK
12+16+26=54
54=54

Hope this helps---ptaylor