SOLUTION: Two identical jars are filled with mixtures of water and vinegar in the ration of 2 to 1 and 3 to 1 respectively. If both jars are emptied into another container, find the ratio of

Question 1120516: Two identical jars are filled with mixtures of water and vinegar in the ration of 2 to 1 and 3 to 1 respectively. If both jars are emptied into another container, find the ratio of water to vinegar in the resulting mixture.
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the first jar has water to vinegar in the ratio of 2/1.

this means 2 parts of water to 1 part of vinegar for a total of 3 parts.

the ratio of water to total mixture in the first jar is therefore 2/3.

the second jar has water to vinegar in the ratio of 3/1.

this means 3 parts of water to 1 part of vinegar for a total of 4 parts.

the ratio of water to total mixture in the second jar is therefore 3/4.

the amount of total mixture in each jar is the same.

if we let x equal the total mixture in each jar, then the amount of water in the first jar is 2/3 * x and the amount of water in the second jar is 3/4 * x.

when you add both jars into a combined jar, the total mount of mixture in the combined jar is 2 * x.

the total amount of water in the combined jar is 2/3 * x + 3/4 * x = 17/12 * x.

the ratio of water to total mixture in the combined jar is therefore (17/12) / 2.

this results in a ratio of water to total mixture in the combined jar of 17/24.

this means there are 17 parts of water and (24 - 17) = 7 parts of vinegar in the combined jar.

this means the ratio of water to vinegar in the combined jar is 17/7.

that's your solution.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Change the ratios to fractions to find the fraction of the combined mixture that is water; then convert that fraction to the ratio the problem asks for.

Let x be the volume of each jar. Then the total volume of the mixture is 2x.

In one jar the amount of water is (2/3)x (ratio 2:1); in the other it is (3/4)x (ratio 3:1). So the total amount of water in the mixture is
(2/3)x + (3/4)x = (17/12)x

Then the fraction of the mixture that is water is
((17/12)x)/(2x) = 17/24

So the ratio of water to vinegar in the mixture is 17:7.
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