eduardofp wrote:

Please help with the following question from PS:

In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 5 : 24. In the company, what is the maximum number of non-managers in a department that has 8 managers:

a) 36

b) 37

c) 38

d) 39

e) 40

Let M = managers

Let x = non-managers

"[T]he ratio of the number of managers to the number of non-managers [] must always be

greater than 5 : 24" -->

\(\frac{M}{x} >

\frac{5}{24}\)

Maximum number of non-managers if there are 8 managers?

\(\frac{8}{x} >

\frac{5}{24}\)

Cross multiply (the numbers are positive):

\((24)(8) > 5x\)

\(192 > 5x\)

\(38.4 > x\), or \(x < 38.4\)

The number of non-managers must be fewer than 38.4 -- AND we want the maximum possible number of non-managers. We need the integer just below 38.4, which is 38.

Answer C

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