Two identical jars are filled with mixtures of water and vinegar in the ratios of 2 to 1 and 3 to 1 respectively. If both jars are emptied into another container then the ratio of water to vinegar in the resulting mixture is.
To find the ratio of water to vinegar in the resulting mixture, we need to calculate the total amount of water and vinegar in both jars and then compare the quantities.
Let's start by assuming the jars have a certain volume. Let's say the volume of each jar is "x" (you can assume any value you like).
In the first jar, the ratio of water to vinegar is 2 to 1, which means for every 2 parts of water, there is 1 part of vinegar. So, in the first jar:
Amount of water = 2/3 * x
Amount of vinegar = 1/3 * x
In the second jar, the ratio of water to vinegar is 3 to 1, which means for every 3 parts of water, there is 1 part of vinegar. So, in the second jar:
Amount of water = 3/4 * x
Amount of vinegar = 1/4 * x
Now, we can add the amounts of water and vinegar from both jars:
Total amount of water = (2/3 * x) + (3/4 * x)
Total amount of vinegar = (1/3 * x) + (1/4 * x)
To find the ratio of water to vinegar in the resulting mixture, we divide the total amount of water by the total amount of vinegar:
Ratio of water to vinegar = (Total amount of water) / (Total amount of vinegar)
Now, we can substitute the values:
Ratio of water to vinegar = [(2/3 * x) + (3/4 * x)] / [(1/3 * x) + (1/4 * x)]
To simplify the expression, we can find a common denominator for the fractions:
Ratio of water to vinegar = [8/12 * x + 9/12 * x] / [4/12 * x + 3/12 * x]
Now, combining like terms in the numerator and denominator:
Ratio of water to vinegar = (17/12 * x) / (7/12 * x)
Simplifying further by canceling out "x":
Ratio of water to vinegar = 17/7
Therefore, the ratio of water to vinegar in the resulting mixture is 17 to 7.
total parts water: 2+3
total parts vinegar: 1+1
final ratio is 5:2