Expert: Sherman D. - 11/9/2005

Question
there are 174 hores stabled for the winter at assinaboine down. the horses are either stallions, colts, mares, or fillies. there are twice as manymares as stallions, half as many colts as stallions, two thirds as many fillies as mares. find the number of each in the stables.

Answer
s = stallions
c = colts
m = mares
f = fillies

m + c + f + s = 174

m = 2s
c = (1/2)s
f = (2/3)m

m = 2s
c = (1/2)s
f = (2/3)(2s) = (4/3)s

m + c + f + s = 174
2s + (1/2)s + (4/3)s + s = 174

multiply everything by 6

12s + 3s + 8s + 6s= 1044
29s = 1044
s = 36

m = 2(36) = 72
f = (4/3)(36) = (144/3) = 48
c = (1/2)(36) = 18
s = 36

ANS :
36 stallions
72 mares
18 colts
48 fillies