Question

This is a probability 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 select a can of cola. There is a 44% chance that the drink selected is diet. How many caffeine-free diet colas are in the cooler?
I know 44/100 = 11/25 is the probability for the 44 drinks and I also know that there are 16 diet, but then I get stuck.

Answer 1

Ah, but there aren't only 16 diet drinks. There are 16 diet drinks PLUS the unknown amount of caffeine-free diets. So we can't know how many total diet drinks there are until we solve the problem!

Let's work through this step by step. Can you set up an equation that will allow you to solve for the amount of diet caffeine-free drinks using the given information?

Answer 2

Okay, let me give it a try. (16+ x/25)=(11/25) Does that work?

Answer 3

Not quite, but you are getting the idea. Remember though, that the 11/25 (or 44%) is the amount of diet drinks out of the TOTAL amount of drinks. So if we were to set up an equation, it would have to be in the same format:

Amount of diet drinks/total amount of drinks = .44

Think about what to fill in for "Amount of diet drinks" and "total amount of drinks" and you'll have it.

Answer 4

Alright, so then idk if this is right or not, but (16+x)(44+x)=0.44?

Answer 5

If you missed a sign in there (I'm assuming that's just a typo), then yes, that is absolutely correct. Remember (just in case it's not a typo!), that you are DIVIDING the "amount of diet" and "total amount of drinks", not multiplying.

But if that's just forgetting the sign, then yes, you are correct:

(16+x)/(44+x) = .44

Now just solve for x.

Answer 6

Oh okay thank you. :) Thank you so much.

Answer 7

You were a lot of help

Answer 8

What did you get for an answer?

Answer 9

x=6

Answer 10

Perfect. If you want to check your answer, just to be extra sure, you can always go back and plug it into your equation and see if you get .44.

Happy to help :)