Question 1205699
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.