Windy Castle
A small number of soldiers live in Windy Castle. Some are infantrymen and and the rest are Cavalry. Soldiers are each allowed to keep a pet pig, and a third of the soldiers do. At the annual banquet, each infantryman ate 12 quails, each cavalryman ate 17 quails and each pig ate 9 quails. Together, soldiers and pigs ate 305 quails. How many pigs are there at Windy Castle?
The answer is 6.
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1 solution
Let I be the number of infantrymen, C the number of cavalrymen, and P the number of pigs. If one-third of the soldiers keeps a pig then I + C = 3 P . The number of quail eaten is Q = 1 2 I + 1 7 C + 9 P = 1 2 ( I + C ) + 5 C + 9 P = 1 2 ( 3 P ) + 5 C + 9 P = 4 5 P + 5 C = 5 ( 9 P + C ) . Since Q = 3 0 5 , we conclude that 9 P + C = 5 3 0 5 = 6 1 . Solutions with positive whole numbers include P = 6 , C = 7 ; P = 5 , C = 1 6 ; etc. Only the first corresponds to a positive value for I . Therefore P = 6 ; C = 7 ; I = 1 1 .