A jar is half full with vinegar and another jar twice its size is one quarter full of vinegar. Both jars are then filled with water. The contents are mixed in a third container. What part of the mixture in the third container is vinegar?
To find out what part of the mixture in the third container is vinegar, we can calculate the total volume of vinegar and water in each jar, and then add them together in the third container. Let's break it down step by step:
Let's assume the first jar's size is 'x'.
1. The first jar is half full with vinegar, so the volume of vinegar present in the first jar is (1/2) * x.
2. The second jar is twice the size of the first jar, so its size is 2 * x.
The second jar is one quarter full of vinegar, so the volume of vinegar present in the second jar is (1/4) * (2 * x) = (1/2) * x.
3. After filling both jars with water, the first jar will have a total volume of x, and the second jar will have a total volume of 2 * x.
Now, let's calculate the total volume of vinegar in the third container after mixing the contents of both jars:
In the first jar, the volume of vinegar is (1/2) * x, and the volume of water is x. So the total volume of the mixture in the first jar is (1/2) * x + x = (3/2) * x.
In the second jar, the volume of vinegar is (1/2) * x, and the volume of water is 2 * x. So the total volume of the mixture in the second jar is (1/2) * x + 2 * x = (5/2) * x.
Finally, when we mix the contents of both jars in the third container, the total volume of vinegar will be:
(3/2) * x + (5/2) * x = (8/2) * x = 4x.
The total volume of the mixture in the third container will be:
x (volume of water in the first jar) + 2 * x (volume of water in the second jar) = 3x.
Therefore, the ratio of vinegar to the total mixture in the third container is:
4x (volume of vinegar) / 3x (total volume of mixture) = 4/3.
So, in the third container, the part of the mixture that is vinegar is 4/3 or approximately 1.33 times the total volume of the mixture.