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# At a certain company, the ratio of managers to directors is 5:3. If 10

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Re: At a certain company, the ratio of managers to directors is 5:3. If 10 [#permalink]
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Bunuel wrote:
At a certain company, the ratio of managers to directors is 5:3. If 10 of the managers become directors, the new ratio will be 7:5. How many managers are currently at the company?

A 30
B 90
C 140
D 150
E 240

m/d ; 5/3
3m=5d
m-10/d+10 = 7/5
solve
we get
m = 150
IMO D
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Re: At a certain company, the ratio of managers to directors is 5:3. If 10 [#permalink]
selim wrote:
Bunuel wrote:
At a certain company, the ratio of managers to directors is 5:3. If 10 of the managers become directors, the new ratio will be 7:5. How many managers are currently at the company?

A 30
B 90
C 140
D 150
E 240

First assume the common unit. let common unit be x.

Managers = 5x
Directors = 3x

$$\frac{5x -10}{3x + 10}$$= $$\frac{7}{5}$$

25x -50 = 21x + 70

x = 30.

Number of managers = 5*30 = 150.

but the current manager is 10 less so shuldnt the ans be 140
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Re: At a certain company, the ratio of managers to directors is 5:3. If 10 [#permalink]
Bunuel wrote:
At a certain company, the ratio of managers to directors is 5:3. If 10 of the managers become directors, the new ratio will be 7:5. How many managers are currently at the company?

A 30
B 90
C 140
D 150
E 240

Current Ratio:5 managers to 3 directors. After 10 managers becomes directors, the ratio is 7 managers to 5 directors.

Need to determine what amount to scale by since this ratio is in its lowest form; managers=5x and directors=3x.

(5x-10)/(3x+10)=7/5 to show 10 managers being promoted to director from the old ratio(5/3) gives use the new ratio, 7/5.

25x-50=21x+70

x=30,scale by 30. Currently 5*30=150 managers and 3*30= 90 directors.

If 10 managers become directors, the new ratio is 140:100. or 7:5

Please critique if you see fit!
Re: At a certain company, the ratio of managers to directors is 5:3. If 10 [#permalink]
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