Mixing It Up
There are two containers A and B filled with mentha oil with different prices and with volumes 140 and 60 liters respectively. Equal quantities are drawn from both A and B in such a manner that the oil drawn from A is poured in into B and oil drawn from B is poured into A. After doing so, the price per liter becomes equal in both containers. What is the (equal) quantity that was drawn?
Image credit: Wikipedia AlfvanBeem
The answer is 42.
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First we must create an equation that will make use of all the information available to us. Assuming the cost of the different mentha oils to be y and x, and the amount of oil drawn from both containers to be k we get the equation :
from here on it is a simple matter of rearranging the terms until we arrive at a form where we can directly compare the coefficient of one term to the coefficient of the opposing term.
so