SOLUTION: 2 unequal jugs are filled with diluted cordial with different concentrations. The first jug has cordial and water in the ratio 2:5 and the second jug has cordial and water in the

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Question 1184038: 2 unequal jugs are filled with diluted cordial with different concentrations. The
first jug has cordial and water in the ratio 2:5 and the second jug has cordial and
water in the ratio 3:7. The contents of the two jugs are then combined.
If the second jug had twice the volume of diluted cordial compared to the first,
what is the ratio of cordial to water in the final mixture?
Found 3 solutions by ikleyn, greenestamps, robertb:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
2 unequal jugs are filled with diluted cordial with different concentrations. The
first jug has cordial and water in the ratio 2:5 and the second jug has cordial and
water in the ratio 3:7. The contents of the two jugs are then combined.
If the second jug had twice the volume of diluted cordial compared to the first,
what is the ratio of cordial to water in the final mixture?
~~~~~~~~~~~~~~~~~~ 

Let's calibrate the volumes in both jugs ADEQUATELY.


First  jug has the volume of cordial 2x per water volume of 5x.

Second jug has the volume of cordial 3y per water volume of 7y.


Here x and y are commonn measures of volumes for liquids in the 1st and the 2nd jugs, respectively.



        According to the condition,  3y = 2(2x),  or  3y = 4x,  i.e.  y = .



So, we can say that 1st jug has the volume of cordial  2x  per water volume of  5x,  while

                    2nd jug has the volume of cordial  3y=4x  per water volume 7y =  = .


Now, in the mixture we have the cordial volume of  2x + 4x = 6x

per water volume of  5x +  =  = .


The ratio of cordial to water in the final mixture is   =  = .    ANSWER

Solved.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


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NOTE: The other tutor interpreted the phrase "the second jug had twice the volume of diluted cordial compared to the first" to mean the amount of ACTUAL cordial in the two jugs was in the ratio 1:2. That is a possible interpretation; my solution below interprets that phrase to mean the amount of DILUTED CORDIAL -- i.e., the total amounts of mixture in the two jugs -- was in the ratio 1:2.

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A 2:5 ratio of cordial to water in the first jug means 2/7 of that diluted cordial is cordial; a 3:7 ratio in the second jug means 3/10 of that diluted cordial is cordial.

The volume of the diluted cordial in the second jug is twice the volume of the diluted cordial in the first, so when the contents are combined 2/3 of the mixture is from the second jug. The fraction of cordial in the final mixture is then



The ratio of cordial to water in the mixture is then 31:(105-31) = 31:74.

ANSWER: 31:74
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
Let L = volume of diluted cordial in jug 1
===> 2L = volume of diluted cordial in jug 2
From the given, jug 1 would be in cordial by volume and in water by volume.
Also from the given, jug 2 would be in cordial by volume and in water by volume.

===> then the ratio of cordial to water in the final mixture is
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