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

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

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23 Oct 2018, 20:59
00:00

Difficulty:

15% (low)

Question Stats:

83% (00:43) correct 17% (01:27) wrong based on 36 sessions

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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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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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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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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

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