Dudeney, Amusements in Mathematics Problem 21 I paid a man a shilling for some apples, but they were so small that I made him throw in two extra apples. I find that made them cost just a penny a dozen less than the first price he asked. How many apples did I get for my shilling?
Suppose you actually got x+2 apples. The price per dozen was 144/(x+2). The original price per dozen was 144/x, so 144/x - 1 = 144/(x+2). Hence x 2 + 2x - 288 = 0. This factorises as (x - 16)(x + 18) = 0. Obviously x is positive, so x = 16. Hence you got 18 apples. Dudeney 1-25 (C) John Scholes jscholes@kalva.demon.co.uk 25 Oct 2002