到最后一步不明白了

faytastic

If x, y, and k are positive numbers such that (x/x+y )(10) + (y/x+y )(20) = k and if x < y, which of the following could be the value of k?

A.    10
B.    12
C.    15
D.    18
E.    30


10X+20Y=KX+KY

X(10-K)=(K-20)Y

(10-K)/(K-20)=Y/X

之后怎么算呢？有人说首先K 必须在10-20之间 其次 10-K的绝对值要大于K-20  所以只能取15-20（不包括15 20）？？？？？这一步是怎么得出的呢？ |10-K|>K-20 应该得出K<15啊

Avengeryzc

|10-K|>|K-20|   这样得出来的k》15   你这个y/x》1

心诚则灵的MM

选18吧，应该。。。

rooneyfang

I solve it by:

(x/x+y )(10) + (y/x+y )(20) = k  =>   (10x+20y)/(x+y)=k   =>   10+10y/(x+y)=k  becuase x<y and x,y are positive intergers =>  1<x<y. we can find the smallest possible value of K by assuming x=y.

10+10y/(x+y)= 10+10y/2y=10+5=15=k.  so the least number we can get for k is 15. however, because x<y. K >15.

please let me know if I get it right or not.

kobemvp

接3L 如果Y取到无限大，那么K=20 所以综上15<K<20

rooneyfang

Thx Kpbemvp