Question

小倩和小玲都有整钱数,小倩对小玲说,如果你给我2元,我是你钱数的n倍,小玲对小倩说,如果你给我n元,我

Answer 1

设两人钱数分别为X、Y,则有

X+2 = N(Y - 2) ……①

Y + N = 2(X - N) ……②

由②式得Y = 2X - 3N,2X = Y+3N 代入①式,得

Y = (7N+4)/(2N-1) = (7N-3.5+7.5)/(2N-1) = 3.5 + 7.5/(2N-1) 是个整数

则2N - 1 = 1、3、5、15

N = 1、2、3、8 ,即N共有四种可能 .

当N = 1时,小倩X = 7,小玲Y = 11

当N = 2时,小倩X = 6,小玲Y = 6

当N = 3时,小倩X = 7,小玲Y = 5

当N = 8时,小倩X = 14,小玲Y = 4