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The present ratio of students to teachers (OG2016)

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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The present ratio of students to teachers (OG2016)

Post Fri May 06, 2016 12:38 pm
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

OA: E

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Post Fri May 06, 2016 3:12 pm
boomgoesthegmat 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?

A) 5
B) 8
C) 10
D) 12
E) 15
I like to use two variables for these "changing ratios" questions.

The PRESENT ratio of students to teachers at a certain school is 30 to 1
Let S = # of students PRESENTLY
Let T = # of teachers PRESENTLY
We can write: S/T = 30/1
Cross multiply to get: (1)(S) = (30)(T)
Simplify: S = 30T

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
In this scenario...
S + 50 = # of students
T + 5 = # of teachers
So, we get: (S + 50)/(T + 5) = 25/1
Cross multiply to get: (S + 50)(1) = (25)(T + 5)
Expand: S + 50 = 25T + 125
Simplify to get: S = 25T + 75

We now have 2 equations with 2 variables:
S = 30T
S = 25T + 75

To solve, replace S in the bottom equation with 30T
We get: 30T = 25T + 75
So: 5T = 75
Solve: T = 15
So, there are PRESENTLY 15 teachers

Answer: E

Cheers,
Brent

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