Question

if the arthimetic mean of x,x+3,x+6,x+9 and x+12 is 10 , then x=?​

Answer 1

Step-by-step explanation:

x+x+3+x+6+x+9+x+12/5=10

5x+30=50

5x=50-30

5x=20

x=4

Answer 2

If the arthimetic mean of x, x+3, x+6, x+9 and x+12 is 10, then find the value of x.

Solution:

$\implies \sf \dfrac{x + (x+3) + (x+6) + (x+9 )+ (x+12) }{5} = 10$

$\implies \sf \dfrac{x + x+3 + x+6 + x+9 + x+12 }{5} = 10$

$\implies\sf \dfrac{5x +30 }{5} = 10$

$\implies\sf \dfrac{5x +30 }{5} = 10$

$\implies\sf 5x +30 = 10 \times 5$

$\implies\sf 5x +30 =50$

$\implies\sf 5x =50 - 30$

$\implies\sf 5x =20$

$\implies\sf x = \dfrac{20}{5}$

$\implies\sf x = \dfrac{ \cancel{{20}}^{4} }{ \cancel5}$

$\implies\sf x =4$

∴ The value of x = $\green{ \underline{ \boxed{ \sf{4}}}}$

Assimilate:

The Arithmetic average of a number of observation or items is called the mean.

If there are n observations are items $\sf x_1, \:x_2, \:x_3, \:x_4, \:........, \: x_n, \:$ then

$\gray{\underline{ \boxed{ \sf{Mean = \dfrac{ Sum \: of \: all \: observations \: are \: items}{Total \: number \:of \:observations\: are\: items} }}}}$

$\sf{ Mean = \dfrac{x_1, \:x_2, \:x_3, \:x_4, \:........, \: x_n, \:}{n} }$

$\sf{Mean = \dfrac{\Sigma x_i}{n} }$

Where the Greek letter sigma ( Σ ) represents the term total sum of all the terms.

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