SOLUTION: A mixture of 12 liters of Chemical A, 16 liters of chemical B and 26 liters of chemical C is required to kill a destructive crop insect. Commercial spray X contains 1, 2, and 2 par

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Question 203003: A mixture of 12 liters of Chemical A, 16 liters of chemical B and 26 liters of chemical C is required to kill a destructive crop insect. Commercial spray X contains 1, 2, and 2 parts, respectively of these chemicals. Commercial spray Y contains only chemical C. Commercial spray Z contains only chemical A and B in equal amounts. How much of each type of commercial spray is needed to get the desired mixture? (Show all your work including any graphs you used.)
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

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