Question 1205699: A 42ml solution contains lemon juice and water in the ratio of 4: 3, respectively. It is added to another solution with same mixture in the ratio of 2:3, respectively. After that, 23 ml solution is taken out and 9ml of lemon juice is added to it, which makes the final quantity of water as 85.71% of lemon juice and they differ by 6ml. Find the total quantity of second solution?
Found 3 solutions by Edwin McCravy, Theo, greenestamps:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
This doesn't make sense:
"which makes the final quantity of water as 85.71% of lemon juice
and they differ by 6ml."
I'll try to figure out what you must have meant. Meanwhile you might
want to repost.
Edwin
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! i've looked at this several ways and i think this might be the way to solve it.
i can't say that i solved it completely, but i did seem to answer the question this way.
the key that i think i found is in the statement "which makes the final quantity of water as 85.71% of lemon juice and they differ by 6 milli-liters.
if you let W equal the amount of water and L equal the amount of lemon juice, that gets you W = .8571 * L.
you are also given that the difference is 6.
from that, you have two equations that need to be solved simultaneously.
they are W = .8571 * L and L - W = 6.
your first equation to solve simultaneously is W = .8571 * L
your second equation to solve simultaneously is L - W = 6
in the second equation, replace W with .8571 * L to get:
L - .8571 * L = 6
combine like terms to get .1429 * L = 6.
solve for L to get L = 6 / .1429 = 41.98740378 milli-liters.
since W = .8571 * L, then L must be 35.98740378 milli-liters.
your final solution is composed of 41.98740378 milli-liters of L and 35.98740378 milli-liters of W = 77.97480756 milli-liters.
to get to this final solution, 9 milli-liters of L from the second solution were added.
that means that the second solution must have been composed of 32.98740378 milli-liters of L before the 9 were added.
the total quantity of the second solution must then have been 32.98740378 + 35.98740378 = 68.97480756 milli-liters before 23 milli-liters of that solution was removed.
add 23 milli-liters of that solution back in and you get a total of 91.97480756 milli-liters in the second solution prior to the 23 milli-liters being taken out and the 9 milli-liters of L being added to it.
the solution, as far as i can tell, is equal to 91.97480756 milli-liters in the second solution, prior to 23 milli-liters of that solution being removed and before 9 milli-liters of L were added to it, based on this logic.
i stopped there because the question was answered by that last calculation as far as i could tell.
the logic appears to be sound so i'll go with that, even though i'm not sure if that is the correct answer, assuming there is one that can be found somewhere.
it's messy, but it is an answer based on the information provided.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Certainly the wording of the problem is poor....
My interpretation is that in the final mixture the amount of water is 85.71% of the amount of lemon juice, and the amount of water is 6ml less than the amount of lemon juice.
In that case, most of the information in the problem is not relevant.
Almost certainly the 85.71% is a decimal approximation of the fraction 6/7. That means the final solution is 6 parts water and 7 parts lemon juice.
6x = amount of water
7x = amount of lemon juice
Those amounts differ by 6ml:
7x-6x = 6
x = 6
The total amount in the second solution is 6x+7x = 13x = 13*6 = 78ml
ANSWER: 78 ml
|
|
|
