[讨论] 9月math173题

sftd

173) x和y 都是正整数，且x(a) 10
(b) 14
(c) 16
(d) 21
(e) 30
参考答案：作者選E
思路: 作者思路: 首先排除b\c\d，将式子合并为10*（x+2y/x+y），因为x1),故10*（x+2y/x+y）至少要大于10，排除a，得e

个人认为应选c

原式化为10[1+y/(x+y)], 分式上下除以y,得10[1+1/(1+x/y)]，
因为0所以15<10[1+1/(1+x/y)]<20

beckyfxie

I agree.

anchoret

great

fyhllj

解的非常好

ruthere

请问这个式子10[1+y/(x+y)] 怎么来的?

原式化为10[1+y/(x+y)], 分式上下除以y,得10[1+1/(1+x/y)]，
因为0 所以15<10[1+1/(1+x/y)]<20

sftd

10(x+2y)/(x+y)=>10(x+y+y)/(x+y)=>10[1+y/(x+y)]

ruthere

thanks.

以下是引用sftd在2003-9-13 16:15:00的发言：
10(x+2y)/(x+y)=>10(x+y+y)/(x+y)=>10[1+y/(x+y)]

rogersun

10x/x+y+20y/x+y
=10+10*y/x+y

since Xis smaller than y

then,y/x+y is bigger than 1/2, but smaller than 1

therefore, 10*y/x+y is bigger than 5, but smaller than 10.

10+10*y/x+y is bigger than 15, but smaller than 20

so, the answer is 16 (C)