SOLUTION: A jar has 54 pieces of candy consisting of 2 types: peppermint and caramel. The probability of randomly picking a peppermint candy is twice as high as picking a caramel. How many

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Question 978616: A jar has 54 pieces of candy consisting of 2 types: peppermint and caramel. The probability of randomly picking a peppermint candy is twice as high as picking a caramel. How many pieces of caramel candy needs to be added to the jar so that the probability of picking a peppermint candy becomes 3/5?

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x=caramel
2x=peppermint
Those are probabilities.
There are 36 peppermint and 18 caramel (54 total). 3x=54, x=18; 2x=36.
I will now add a pieces of caramel until the fraction of peppermint is now
18+a/54+a will be 2/5, since if the probability of peppermint is 3/5, caramel will be 2/5.
Cross multiply: 2(54+a)=5(18+a)
108+2a=90+5a
18=3a
6=a
add 6 pieces of caramel, and total is 60.
36 are peppermint.
That is 3/5.