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In a certain class, x students are 10 years old, and the remaining y s

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In a certain class, x students are 10 years old, and the remaining y s  [#permalink]

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New post 23 Oct 2018, 20:59
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In a certain class, x students are 10 years old, and the remaining y students are 11 years old. What is the average (arithmetic mean) age of all students in the class?


A. \(\frac{x+y}{21}\)

B. \(\frac{10x+11y}{21}\)

C. \(\frac{110xy}{x+y}\)

D. \(\frac{110xy}{xy}\)

E. \(\frac{10x+11y}{x+y}\)

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Re: In a certain class, x students are 10 years old, and the remaining y s  [#permalink]

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New post 23 Oct 2018, 21:58
Total number of students is x+y

No if students of 10 years old is x. So total age of x students is 10x

No if students of 11 years old is y. So total age of y students is 11y.

Now average is \(\frac{10x+11y}{x+y}\)
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In a certain class, x students are 10 years old, and the remaining y s  [#permalink]

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New post 23 Oct 2018, 22:21
Bunuel wrote:
In a certain class, x students are 10 years old, and the remaining y students are 11 years old. What is the average (arithmetic mean) age of all students in the class?


A. \(\frac{x+y}{21}\)

B. \(\frac{10x+11y}{21}\)

C. \(\frac{110xy}{x+y}\)

D. \(\frac{110xy}{xy}\)

E. \(\frac{10x+11y}{x+y}\)


\(Average \ Age = \frac{Total \ Age \ of \ x \ students + Total \ Age \ of \ y \ students}{Total \ No \ of \ Students}\)

\(Average \ Age = \frac{10x + 11y}{(x + y )}\); Answer must be (E)
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Re: In a certain class, x students are 10 years old, and the remaining y s  [#permalink]

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New post 24 Oct 2018, 02:53

Solution


Given:
    • x students are 10 years old
    • Remaining, y, students are 11 years old

To find:
    • The average age of all students in the class

Approach and Working:
    • Total number of students in the class = x + y
    • Sum of ages of x students = 10x
    • Sum of ages of remaining , y, students = 11y
    • Sum of ages of all the students in the class = 10x + 11y
    • Thus, Average age of all students = \(\frac{(10x + 11y)}{(x + y)}\)

Hence the correct answer is E

Answer: E

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Re: In a certain class, x students are 10 years old, and the remaining y s &nbs [#permalink] 24 Oct 2018, 02:53
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