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The average age of a class, including the teacher is 1.5 years more th

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cfc198
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The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   09 Apr 2019, 11:13
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The average age of a class, including the teacher is 1.5 years more than the average age of the class when the teacher is not considered. If the teacher is 30 years older than the average age of the students, find the number of students in the class.

(1) 27
(2) 24
(3) 20
(4) 19
(5) 18
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D
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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   13 Apr 2019, 18:36
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cfc198 wrote:
The average age of a class, including the teacher is 1.5 years more than the average age of the class when the teacher is not considered. If the teacher is 30 years older than the average age of the students, find the number of students in the class.

(1) 27
(2) 24
(3) 20
(4) 19
(5) 18



We can let n = the number of students and x = the average age of the students. So we have:

(30 + x + nx)/(n + 1) = x + 1.5

30 + x + nx = (x + 1.5)(n + 1)

30 + x + nx = nx + x + 1.5n + 1.5

30 = 1.5n + 1.5

1.5n = 28.5

n = 19

Answer: D/4
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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   11 Sep 2019, 07:48
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According to the question, the teachers age is 30 more than the average age of all students. Thus including the age of the teacher increases the average age by 1.5 years. Divide 30 by 1.5 to get 20 as the total number of people in class including the teacher. Hence the number of students is 19.
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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   11 Sep 2019, 08:15
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cfc198 wrote:
The average age of a class, including the teacher is 1.5 years more than the average age of the class when the teacher is not considered. If the teacher is 30 years older than the average age of the students, find the number of students in the class.

(1) 27
(2) 24
(3) 20
(4) 19
(5) 18


Let n be number of students and let x be average age of a student excluding teacher.

x n + x + 30 = (n+1) (x + 1.5)
x (n+1) + 30 = x (n+1) + 1.5 (n+1)
n+1 = 30/1.5 = 20
n = 19

IMO D
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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   10 Apr 2019, 06:26
cfc198 wrote:
The average age of a class, including the teacher is 1.5 years more than the average age of the class when the teacher is not considered. If the teacher is 30 years older than the average age of the students, find the number of students in the class.

(1) 27
(2) 24
(3) 20
(4) 19
(5) 18


anyone have a solution for this?
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Kunal112
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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   11 Sep 2019, 05:27
Sum of students age's = S No. of students = n Average = x Age of teacher = x + 30
S/n = x (Statement 1)

Also, (S + x + 30)/(n + 1) = x + 1.5 (It is given that average with teacher is 1.5 more than regular average)

(nx + x + 30) = (n + 1)(x + 1.5) here we substituted S = nx from statement 1
Solving this we will get

n = 19

Option D is correct
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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   11 Sep 2019, 08:16
cfc198 wrote:
The average age of a class, including the teacher is 1.5 years more than the average age of the class when the teacher is not considered. If the teacher is 30 years older than the average age of the students, find the number of students in the class.

(1) 27
(2) 24
(3) 20
(4) 19
(5) 18



Please change the answer choices as below:-

(A) 27
(B) 24
(C) 20
(D) 19
(E) 18
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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   11 Sep 2019, 08:22
cfc198 wrote:
The average age of a class, including the teacher is 1.5 years more than the average age of the class when the teacher is not considered. If the teacher is 30 years older than the average age of the students, find the number of students in the class.

(1) 27
(2) 24
(3) 20
(4) 19
(5) 18


So, 30/1.5 = 20 is the total members including the teacher.

So, The number of members in the class excluding the teacher is 20-1 = 19 , Answer must be (4)
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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   11 Sep 2019, 08:51
the teachers age is divided such that the average age,including the teacher's increases by 1.5 . So we get 30/1.5=20 so 20 people had 1.5 added to their average age.
This includes the teacher so we will take him out and get 19.

answer is D
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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink] New post   16 Aug 2023, 16:32
Let y be sum of students age

and n be number of students

Let teacher's age be x

y+x/n+1 - y/n = 1.5

Second statement

x = y/n + 30

xn = y +30n

From the first equation.

y + x - y(n+1)/n = 1.5(n+1)

yn + xn - y(n+1) = 1.5n(n+1)

Sub for xn

ny + y + 30n -yn - y = 1.5n^2 + 1.5n

30n - 1.5n = 1.5n^2

28.5 = 1.5n

n = 19

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Re: The average age of a class, including the teacher is 1.5 years more th [#permalink]
16 Aug 2023, 16:32
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