Do the following problem from Alcuin of York A cask is fille

Do the following problem from Alcuin of York: A cask is filled to 100 metreta capacity through three pipes. One-third of its capacity plus 6 modii flows in through one pipe, one-third of its capacity flows in through another pipe, but only one-sixth of its capacity flows in through the third pipe. How many sextarii flow in through each pipe. (A metreta is 72 sextarii and a modius is 200 sextarii)

Solution

Total capacity of the cask ( in sextarii) = 100 x 72 = 7200 sextarri

Total amount by first pipe = 1/3 of its capacity + 6 modiis = 7200/3+6(200) = 2400+1200 = 3600 sextarri

Total amount by second pipe = 1/3 of its capacity = 7200/3 = 2400 sextarri

So clearly totl amount flow by third pipe = 7200 - 2400 - 3600 = 1200 sextarri

So required answer is 1200 sextarri.