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This Situation is Debata"Bull"!

The son had a herd of bulls and cows, all of which were white, grey, yellow, or piebald. The number of piebald bulls was less than the number of white bulls by five-sixths of the number of grey bulls; it was less than the number of grey bulls by nine-twentieths of the number of yellow bulls; and it was less than the number of yellow bulls by thirteen forty-secondths of the number of white bulls. The number of white cows was seven-twelfths of the number of grey bulls and cows together; the number of grey cows was nine-twentieths of the number of yellow bulls and cows; and the number of piebald cows was thirteen forty-secondths of the number of white bulls and cows. Find the number of the herd?

Solution:

Source: Archimedes, 250 B.C.