请教prep ds1-147由平均数推出比重的问题

147.    14800-!-item-!-187;#058&010134

Each employee on a certain task force is either a manager or a director.  What percent of the employees on the task force are directors?

(1) The average (arithmetic mean) salary of the managers on the task force is $5,000 less than the average salary of all employees on the task force.

(2) The average (arithmetic mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force.

答案：C

我自己在草稿上列出两个方程式，可是怎么可能由这两个条件得到人数比例呢？

有M 个manager,D个directer，他们的平均工资是X，Y

条件1可以知道Y- X=5000

条件2可以知道Y-（Y*D+X*M）/M+D=15000 通分就可得M*（Y-X）/M+D=15000

题目要求得是D/M+D=1-M/M+D

条件1+条件2 可以推出，所以选C

我自己做的，不知道对不对~

谢谢ls!

条件2：X-(YD+XM)/(M+D)=15000

条件1：(YD+XM)/(M+D)-Y=5000

联立可得：D/M=3