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In a certain company, the ratio of the number of managers to

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Manager
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In a certain company, the ratio of the number of managers to [#permalink]

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New post 14 Aug 2008, 22:11
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In a certain company, the ratio of the number of managers to the number of production-line workers in 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

a. 5
b. 10
c. 15
d. 20
e. 25

Please elaborate on how to solve (1) algebraically then (2) fastest. Thx.

Kudos [?]: 122 [0], given: 0

Manager
Manager
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Joined: 27 Mar 2008
Posts: 81

Kudos [?]: 122 [0], given: 0

Re: PS: Manager v. Worker (proportions) [#permalink]

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New post 15 Aug 2008, 10:37
alpha_plus_gamma wrote:
droopy57 wrote:
In a certain company, the ratio of the number of managers to the number of production-line workers in 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

a. 5
b. 10
c. 15
d. 20
e. 25

Please elaborate on how to solve (1) algebraically then (2) fastest. Thx.


72 * M = 5 * W
74 * M = 5 * W + 40

M = 20




Thanks. I didn't see that I could substitute until I broke down the question step by step...

Kudos [?]: 122 [0], given: 0

Manager
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Joined: 30 Jul 2007
Posts: 129

Kudos [?]: 22 [0], given: 0

Re: PS: Manager v. Worker (proportions) [#permalink]

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New post 15 Aug 2008, 11:05
droopy57 wrote:
alpha_plus_gamma wrote:
droopy57 wrote:
In a certain company, the ratio of the number of managers to the number of production-line workers in 5 to 72. If 8 additional production-line workers were to be hired, the ratio of the number of managers to the number of production-line workers would be 5 to 74. How many managers does the company have?

a. 5
b. 10
c. 15
d. 20
e. 25

Please elaborate on how to solve (1) algebraically then (2) fastest. Thx.


72 * M = 5 * W
74 * M = 5 * W + 40

M = 20




Thanks. I didn't see that I could substitute until I broke down the question step by step...


Also, a fast way if you're pressed for time:

If an increase of 8 resulted in a ratio increase of 2, then the true total of each set must be a multiple of 4. So 5*4 = 20

Kudos [?]: 22 [0], given: 0

Manager
Manager
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Joined: 30 Jul 2007
Posts: 129

Kudos [?]: 22 [0], given: 0

Re: PS: Manager v. Worker (proportions) [#permalink]

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New post 15 Aug 2008, 14:00
droopy57 wrote:
sarzan wrote:

Also, a fast way if you're pressed for time:

If an increase of 8 resulted in a ratio increase of 2, then the true total of each set must be a multiple of 4. So 5*4 = 20



Can you expand on this?


The ratio of Managers to Workers was 5 to 72, and after adding 8 more Workers, the ratio became 5 Managers to 74 Workers. Since no more Managers were added, this tells us that adding 8 more Workers contributed only 2 to the Workers ratio (you can think of it as a sub-ratio), and so if 2 gives you 8, then 5 must give you 20.

Here's another way to think of it:

If the ratio of police officers to criminals is 1 to 2, respectively, and if 50 more criminals were added to the city, resulting in a new ratio of police to criminals of 1 to 4, while no police officers were added or subtracted, then how many officers are there?

This tells us that a ratio of 2 gives you 50, and so there are 25 police officers.

I hope this doesn't confuse you. I would only do this if I am pressed for time.

Kudos [?]: 22 [0], given: 0

Re: PS: Manager v. Worker (proportions)   [#permalink] 15 Aug 2008, 14:00
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In a certain company, the ratio of the number of managers to

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