Letter: Puzzle answered

From Stuart Semmens

I read Stephanie Pain’s article on ancient Chinese mathematics with interest, but I can’t figure out the initial problem about the fox, the wildcat and the dog (29 July, p 50).

What is the answer, and how is it arrived at?

Stephanie Pain writes:

• If the cat’s skin is worth twice the dog’s and the fox’s worth twice the cat’s, then the dog pays one-seventh of the total, the cat two-sevenths and the fox four-sevenths. Divide the total amount owed (“111 cash”) by seven, to give the dog’s share (15 and 6/7ths cash). Multiply this by two to give the cat’s share (31 and 5/7ths cash), and by four for the fox’s (63 and 3/7ths cash).

Selby, Victoria, Australia