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The average age of 28 students is 9 yr. If the age of their teacher is

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Bunuel
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The average age of 28 students is 9 yr. If the age of their teacher is [#permalink] New post   26 Jan 2021, 05:45
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The average age of 28 students is 9 yr. If the age of their teacher is included, it becomes 10 yr. The age of the teacher (in years) is :


(A) 27
(B) 31
(C) 38
(D) 40
(E) 41
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C
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meanup
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Re: The average age of 28 students is 9 yr. If the age of their teacher is [#permalink] New post   26 Jan 2021, 08:53
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\(Difference \ in \ Average =9-10=-1\)

Equation;

\(-1*28 + 1*x = 10\)

\(x=10+28=38\)

Ans C
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sofiaeisenacht
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Re: The average age of 28 students is 9 yr. If the age of their teacher is [#permalink] New post   26 Jan 2021, 15:34
You can solve it by using the average formula.

The statement says that the new average (when the teacher is included) is 10 years old. You also have the average of 28 students. What you need to find is the teacher´s age, that is the only thing you don´t know.

Let´s represent the teacher´s age by the letter t. You know that there are 28 students, so when adding the teacher to the equation, you need to divide everything by 29, that is the new total of people. Remember that 9 years old is the average without considering the teacher, so you will need to multiply it by 28.

10 = (28x9 + t)/ 29
When you solve it, the answer is 38 years old.
Answer C
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Re: The average age of 28 students is 9 yr. If the age of their teacher is [#permalink] New post   26 Jan 2021, 18:27
I use weight average formula to solve this question.

Formular : \([\frac{(A member)}{(all members)}*(average of A)]\) + \([\frac{(B member)}{(all members)}*(average of B)]\) = average of A and B

We know the number of students in class and assume that there is 1 teacher per class to make it easy to calculate.
So now we know :
Number of all member in class - 28+1
The ratio of student - \(\frac{ 28}{29 }\)
Ratio of teacher - \(\frac{1}{29}\)
Average age of student - 9
Average age of teacher - X
Average of Student and Teacher - 10

Apply the formula


\(\frac{28}{29}*(9) + \frac{1}{29}*(x)\) = 10
\(\frac{252}{29}+ \frac{x}{29}\) = 10
252+x = 290
x = 38

Answer C

This is my first time comments on solving question. Hope this comment is helpful!
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Re: The average age of 28 students is 9 yr. If the age of their teacher is [#permalink]
26 Jan 2021, 18:27
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