A man had a 10-gallon keg full of wine, and an empty jug. On Monday he drew off a jugful of wine and filled up the keg with water. On Friday, after the wine and water had been thorougly mixed, he drew off another jugful and again filled up the keg with water. The keg then contained equal quantities of wine and water.

What was the capacity of the jug?

Let x be the capacity of the jug (in gallons).

On Monday he will draw x gallons of wine out and leave 10-x gallons of wine in the keg.

On Friday he will draw x/10 * 10-x = (10x - x²)/10 gallons of wine out of the keg, and this will leave 5 gallons of wine.

Therefore, the two amounts must equal 5.

x + (10x - x²)/10 = 5

10x + 10x - x² = 50

x² - 20x + 50 = 0

solve for x and we get ~2.92893 gallons

*** edited typo, answer remains the same

Edited on July 14, 2004, 1:43 pm

Posted by Thalamus on 2004-07-14 13:05:08