SOLUTION: A glass is half full of pure alcohol. A second glass whose volume is twice the volume of the first glass is one-third full of pure alcohol. Both glasses are then filled to the top

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Question 283351: A glass is half full of pure alcohol. A second glass whose volume is twice the volume of the first glass is one-third full of pure alcohol. Both glasses are then filled to the top with water and mixed together in a third container. What fraction of the final mixture is alcohol?
A 5/6 b 5/12 c 7/12 d 5/18 e 7/18

Answer by Theo(13342) About Me  (Show Source):
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let the volume of the first glass be x
let the volume of the second glass be 2x
the volume of the container is 3x.

The amount of alcohol in the first glass is (1/2)*x
The amount of alcohol in the second glass is (1/3)*2x = (2/3)*x
The total amount of alcohol in the container is (1/2)*x + (2/3)*x = (3/6)*x + (4/6)*x = (7/6)*x
The total volume of the container is 3*x.
The fraction of alcohol in the container is therefore (7/6)*x / (3*x) which is equal to (7/18).

As an example:

Assume the first glass is 6 ounces.
It is half full of alcohol so this contains 3 ounces of alcohol.

The second glass is twice the volume of the first glass so the volume of the second glass is 12 ounces.
It is 1/3 full of alcohol so this contains 4 ounces of alcohol.

The total alcohol in both glasses is 3 ounces + 4 ounces = 7 ounces.

The total volume of the mixture in the container is 6 ounces + 12 ounces = 18 ounces.

The fraction of alcohol in the container is 7 ounces / 18 ounces = 7/18