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The present ratio of students to teachers at a certain

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Manager
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Joined: 14 Dec 2011
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The present ratio of students to teachers at a certain [#permalink] New post 26 Mar 2012, 02:48
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

76% (02:39) correct 23% (01:41) wrong based on 134 sessions
The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

(A) 5
(B) 8
(C) 10
(D) 12
(E) 15

[Reveal] Spoiler:
This might be really embarrasing, since I normally score Q47 or higher, but this question really made me stumble.

What is wrong with my approach (I always use this approach on ratio questions and it normally works well):

Plug in E:

25:1 is the new ratio -> 1 = 1*15 = 15 teachers and 25 = 25*15 = 375 students

15 - 5 = 10 teachers before the increase
375 - 50 = 325 students before the increse

so the old ratio is 325 : 10 which is unequal to 30:1

Where is my mistake?

PS. No need to tell me others ways how to solve it. I am familiar with the 'equations ways'.


Cheers a lot and I am happy ti give away Kudos ;)
Lars
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Dec 2012, 05:59, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Slightly embarrasing [#permalink] New post 26 Mar 2012, 03:02
4
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Expert's post
Impenetrable wrote:
The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers ?

5
8
10
12
15


This might be really embarrasing, since I normally score Q47 or higher, but this question really made me stumble.

What is wrong with my approach (I always use this approach on ratio questions and it normally works well):

Plug in E:

25:1 is the new ratio -> 1 = 1*15 = 15 teachers and 25 = 25*15 = 375 students

15 - 5 = 10 teachers before the increase
375 - 50 = 325 students before the increse

so the old ratio is 325 : 10 which is unequal to 30:1

Where is my mistake?

PS. No need to tell me others ways how to solve it. I am familiar with the 'equations ways'.


Cheers a lot and I am happy ti give away Kudos ;)
Lars


The very first step is not correct: the present ratio of students to teachers is 30 to 1, not 25 to 1. So if you want to plug t=15 you should use 30:1 ratio, not 25:1.

Complete solution:

Given: \frac{s}{t}=\frac{30x}{x} and \frac{30x+50}{x+5}=\frac{25}{1}. Solve \frac{30x+50}{x+5}=\frac{25}{1} for x --> x=15 --> t=x=15.

Answer: E.

Hope it helps.
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Manager
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Re: The present ratio of students to teachers at a certain [#permalink] New post 26 Mar 2012, 03:14
How stupid of me. I should slap myself.


Thanks a lot! ;)
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Re: The present ratio of students to teachers at a certain [#permalink] New post 26 Mar 2012, 03:16
2
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+1 E

Here's what I did
s/t = 30/1 => s=30T

S+50/t+5 = 25/1

Substitute S=30T in the above equation

30t+50 = 25t+125

5t = 75
t=15

I hope this helps. By the way I was facing the same situation & it helps if you just take a break. I couldnt even recognise simple s v errors :-p
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Manager
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Re: The present ratio of students to teachers at a certain [#permalink] New post 25 Oct 2012, 01:28
I actually thought it would be easier to tackle this problem by plugging in the answers choices, but I was VERY wrong, it's just tedious and prone to errors for this exercise.

Straight algebra saves you at least 1 full minute and it's very simple in this case.

Thanks to Bunuel for the clarifications.
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Re: The present ratio of students to teachers at a certain [#permalink] New post 09 May 2013, 18:51
the first part seems to be the trickiest,\frac{S}{T} = \frac{30}{1}, then cross multiply to get 30T=S
Re: The present ratio of students to teachers at a certain   [#permalink] 09 May 2013, 18:51
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