Theres 12 reg, 8 cherry, 10 diet, 6 diet cherry, 8 0-caf and some 0-caf diet 44% chance that the drink is diet. How many 0-caf diet colas?

Question

Full Question: A picnic cooler contains different types of cola: 12 regular, 8 cherry, 10 diet, 6 diet cherry, 8 caffeine-free, and some caffeine-free diet. You pick a can of cola without looking at its type. There is a 44% chance that the drink selected is diet. How many caffeine-free diet colas are in the cooler?

I don't really understand what the question is asking, just looking for some help.

Answer 1

12 regular (not diet) 

8 cherry (not diet) 

10 regular diet 

6 diet cherry 

8 caffiene-free (assuming not diet) 

X  caffiene free diet 

number  non-diet = 12 + 8+ 8 =    28  

number diet  =   10+ 6 +  X  = 16+ X 

Total Cans  =   28+ 16 + x =   44+ X   

Percent diet  =  (16+X)/ (44 + X) 

44/100  = (16+X)/ (44+ X)  

44(44 + X) = (16 + X)100 

1936 + 44X  = 100X + 1600 

56X = 1936-1600 =  336 

X = 336/56 =   6   

6 can of caffeine free diet cola are in the cooler. 

this means 22 of the 50 cans were diet  

22/50 = 46/100 so 46 percent