Dudeney, Amusements in Mathematics Problem 19 The proprietor of a small London cafe has given me some interesting figures. He says that the ladies who come alone to his place for refreshment spend each on an average eighteenpence, that the unaccompanied men spend half a crown each, and that when a gentleman brings in a lady he spends half a guinea. On New Year's Eve he supplied suppers to twenty-five persons and took five pounds in all. Now, assuming his averages have held good in every case, how was his company made up on that occasion? Of course, only single gentlemen, single ladies, and pairs (a lady and a gentleman) can be supposed to have been present, as we are not considering larger parties.
Let the number of single ladies, single gentlemen and pairs be L, G, P respectively. Then L + G + 2P = 25 and 18L + 30G + 126P = 1200. Hence 12G + 90P = 750. That gives P = 1, 3, 5, or 7. But L must be non-negative, so P = 7, giving G = 10, L = 1. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002