GMAT, GRE Quant Mixture Problem

How must a grocer mix 4 types of peanuts worth 54 c, 72 c, $1.2 and $1.44 per pound so as to obtain a mixture at 96 cents per pound?

(A) 8:4:4:7
(B) 24:12:12:50
(C) 4:8:7:4
(D) 16:42:28:10
(E) Cannot be uniquely determined

Price in cents of the 4 types of peanuts: 54, 72, 120, 144

Ratio of the price of 4 types of peanuts 9 : 12 : 20 : 24

Average Price of mixture = 96 cents
Average Price of mixture = 16 parts if you reduce the original amount by dividing by 6.

[Price (in cents) of 4 types of peanuts 54:72:120:144 eq. (1)
Ratio of Price of 4 types of peanuts 9 : 12 : 20 : 24 parts eq. (2)
Multiply equation (2) by 6 , you will get equation (1).]

Time to Plug in the options that are available:
The sum (Respective Quantity x Respective Price) = Total Price = Average price x Total Quantity

Option 1
Ratio for the quantities - 8a:4a:4a:7a
Total quantity = 23a parts (8+4+4+7)
(8a.9 + 4a.12 + 4a.20 + 7a.24) = 16.23a
368a = 368a
LHS = RHS
Thus option 1 satisfy the condition

Option 2
Ratio for the quantities - 24a:12a:12a:50a or 12a:6a:6a:25a
Total quantity = 49a parts
(12a.9 + 6a.12 + 6a.20 + 25a.24) = 16.49a
900a = 784a
LHS is not equal to RHS
Thus option 2 does not satisfy the condition

Option 3
Ratio for the quantities - 4a:8a:7a:4a
Total quantity = 23a parts
(4a.9 + 8a.12 + 7a.20 + 4a.24) = 16.23a
368a = 368a
LHS = RHS
Thus option 3 satisfy the condition

They asked for a unique case so a problem can't have two solutions. So it cannot be determined

E