Question

数学题 求未知数

一个3心淘宝买家 购物次数在（41-90之间） 给出的好评率是80.56% ，求他一共给过多少个差评，一共购物多少次、。求算法。谢谢

Answer 1

设总共购物x次，x是整数，好评次数：
80.56%x，也是整数，或者最接近的整数。
80.56%（41~90）=33.0296~72.504
整数问题，可以用连分数来解
80.56%=8056/10000=1007/1250=（19×53）/（2×5^4)
=1/(1+243/1007)
=1/(1+1/(4+35/243))
=1/(1+1/(4+1/(6+33/35)))
=1/(1+1/(4+1/(6+1/(1+2/33))))
=1/(1+1/(4+1/(6+1/(1+1/(16+1/2)))))
渐进分数：
1/（1+0）=1
1/(1+1/4）=4/5
1/(1+1/(4+1/6））=25/31
1/(1+1/(4+1/(6+1/1）））=29/36
1/(1+1/(4+1/(6+1/(1+1/16））））=489/607
1/(1+1/(4+1/(6+1/(1+1/(16+1/2)))))=1007/1250
在分母为41~90之间，只有29/36
x=36，好评29，好评率=29/36=80.5555555555555556%≈80.56%
差评36-29=7