Question

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If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m?
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Answer 1

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$\large\mathsf\red{Q \ - \ What \ is \ Mean \ ?}$

$\mathsf\blue{Mean \ is \ the \ total \ of \ all \ values \ divided}$
$\mathsf\blue{by \ the \ number \ of \ values.}$

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$\large\mathsf\green{Given \ -}$

$\mathsf{x \ is \ mean \ of \ m \ and \ 9.}$

•°•

$\mathsf{x \ = \ (m + 9) / 2}$

$\mathsf{Also,}$

$\mathsf{y \ is \ the \ mean \ of \ 2m \ and \ 15.}$

•°•

$\mathsf{y \ = \ (2m + 15)/2}$

$\mathsf{Also,}$

$\mathsf{z \ is \ the \ mean \ of \ 3m \ and \ 18.}$

•°•

$\mathsf{z \ = \ (3m + 18)/2}$

$\mathsf{Now,}$

$\mathsf{x + y + z \ -}$

$\mathsf{= \ (m + 9) / 2 + (2m + 15)/2 + (2m + 15)/2}$

$\mathsf{= \ (6m + 42)/2}$

$\mathsf{= \ 3m + 21}$

$\mathsf{Average \ of \ x, \ y \ and \ z}$

$\mathsf{= \ (3m + 21)/3}$

$\large\mathsf\green{= \ m + 7}$

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Answer 2

Answer:

$\huge{Correct \: Question :-}$

If x is the average ( arithmetic mean ) of m and 9, y is the average of 2m and 15 and z is the average of 3m and 18, what is the average of x,y and z in terms of m ?

$\huge{Solution :-}$

Average = (Sum of All observation ) / (Total Number of observation).

Case ❶ :-

x is the average of m & 9 ..

So ,

➼ x = (m + 9)/2 ---------------- Equation (1) .

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Case ❷ :-

y is the average of 2m and 15..

So,

➪ y = (2m + 15)/2 -------------- Equation (2) .

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Case ❸ :-

z is the average of 3m and 18 .

So ,

➳ z = (3m + 18)/2 ------------- Equation (3).

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Now, Average of x , y and z :-

➻ (x + y + z) /3

Putting value of x ,y & z from Equation (1), (2) & (3),

➻[ (m + 9)/2 + (2m+15)/2 + (3m+18)/3 ]

➻ [ (m + 9 + 2m + 15 + 3m + 18) / 3 ]

➻ [ (6m + 42) /2*3 ]

➻ [6 (m + 7) /6 ]

➻ [ (m + 7) ]

➻ (m + 7) (Option B). (Ans).