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The present ratio of students to teachers at a certain school is 30 to
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13 Jan 2022, 09:14
13 Jan 2022, 09:14
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Question Stats:
91% (01:41) correct
8% (01:33) wrong based on 12 sessions
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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
(A) 5
(B) 8
(C) 10
(D) 12
(E) 15
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Re: The present ratio of students to teachers at a certain school is 30 to
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13 Jan 2022, 11:01
13 Jan 2022, 11:01
Carcass 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
(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
Re: The present ratio of students to teachers at a certain school is 30 to
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13 Jan 2022, 12:09
13 Jan 2022, 12:09
1
I'd plug answers, D first then B: lets say 12 teachers(30:1) so number of students 12×30=360. Now new ratio 12+5 & (25:1) so now students 17×25=425, 425-360 = 65 falling short by a few numbers so let's plug Option E, 15 case 1(30:1) so students = 450 and 2nd case 20 (25:1), so students = 500 and 500-450 = 50.
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