A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch? Choose the correct choice from the following answers: A) 34 B) 38 C) 42 D) 46 E) 50
5/7*P are ponies with horseshoes, so P is a multiple of 7.   2/3*5/7*P = 10/21*P are Icelandic ponies with horseshoes, so P is a multiple of 21.   The minimum value of P is 21. Then H = P+4 = 25.   The minimum number of horses and ponies is 46.   The answer is 46.
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A ranch has both horses and ponies. Exactly 5/7 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?