Question

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

Answer 1

Answer:

$Value \:of\: x = 4$

Step-by-step explanation:

$Given \: observations \:are \:\\x,x+3,x+6,x+9 \: and \: x+12 \: is \: 10$

$\boxed {Mean(x)=\frac{Sum\:of\: observations}{Number \: of \: observations}}$

$Mean=10$

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

$\implies \frac{5x+30}{5}=10$

$\implies \frac{5(x+6)}{5}=10$

$\implies x+6=10$

$\implies x = 10-6$

$\implies x = 4$

Therefore,

$Value \:of\: x = 4$

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Answer 2

Given numbers are

$x \\ x + 3 \\ x + 6 \\ x + 9 \\ x + 12$

The arithmetic mean of the given numbers is

$10$

We need to find the value of x.

We know that the arithmetic mean is

$mean = sum \: of \: observations \div total \: number \: of \: observations$

By substituting the values,

$10 =( x + x + 3 + x + 6 + x + 9 + x + 12) \div 5 \\ 10 \times 5 = 5x + 30 \\ 50 = 5x + 30 \\ 5x = 50 - 30 \\ 5x = 20 \\ x = 20 \div 5 \\ x = 4$

Therefore, the value of x is 4.

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