A jar is half full of 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?
Let volume of first jar = v
Volume of second jar = 2v
Volume of vinegar in first jar = v/2
volume of vinegar in second jar = 2v/4 = v/2
Sum of volume of both jars = v+2v = 3v
Sum of volume of vinegar = v/2+v/2 = v
Can you take it from here?
2v
To determine the part of the mixture in the third container that is vinegar, we first need to calculate the amount of vinegar in each jar.
Let's assume that the first jar has a capacity of 1 unit (for example, 1 liter) and initially contains half of it with vinegar, which is 1/2 unit of vinegar.
Since the second jar is twice the size of the first jar, its capacity would be 2 units. And if it is one quarter full of vinegar, it contains 1/4 unit of vinegar.
Now let's find out how much water is added to each jar. Since both jars are completely filled with water after adding it, we can calculate the amount of water in each jar.
For the first jar, since it initially contained 1/2 unit of vinegar, the rest of the jar must be filled with 1/2 unit of water.
For the second jar, since it initially contained 1/4 unit of vinegar, the rest of the jar must be filled with 2 - 1/4 = 7/4 units of water.
Now we can calculate the total amounts of vinegar and water in the third container after mixing the contents of the two jars.
The total amount of vinegar in the third container is 1/2 + 1/4 = 3/4 units (from both jars).
The total amount of water in the third container is 1/2 + 7/4 = 9/4 units (from both jars).
The sum of the vinegar and water in the third container is 3/4 + 9/4 = 12/4 = 3 units.
Therefore, the part of the mixture in the third container that is vinegar is 3/3 = 1 unit, or 100%.