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# Each employee on a certain task force is either a manager or

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Intern
Joined: 25 Jul 2007
Posts: 16
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Kudos [?]: 6 [0], given: 0

Each employee on a certain task force is either a manager or [#permalink]  27 Oct 2007, 10:33
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 $5000 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.

I've put way too much time into this and can't figure it out--thanks!
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 127 [0], given: 0

M = number of managers.
D = number of directors.
N = total employees.
X = average salary.

since:

NX = total salary

M(x-5000)+D(x+15000) = NX

MX-M5000+DX+D15000 = NX

and since:

M+D = N

then

MX+DX = NX

so:

-M5000+D15000 = 0

D15000 = M5000

3D = M

for every three directors you have one manager.

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