# 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?

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.

### 1 Answer

- AlanLv 71 month ago
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