Question

If the mean of 2x +3, 3x+4,x+7,x-3 4x-7 is 14 find x

Answer 1

Answer:

$\large{\underline{\boxed{\sf x = 6}}}$

Step-by-step explanation:

Given ;

Observations = 2x + 3, 3x + 4, x + 7, x - 3, 4x - 7.

No. of observations = 5

Now, we know that ;

$\bf Mean = \dfrac{Sum \: of \: observations}{Number \: of \: observations}$

We need to find the sum of observations:

⇒ 2x + 3 + 3x + 4 + x + 7 + x - 3 + 4x - 7

⇒ 11x + 14 - 10

⇒ 11x + 4

So,

$\bf Mean = \frac {sum \: of \: observations}{No. \: of \: observations}\\\\\sf \implies \frac{11x + 4}{5}=14\\\\\bf On \: cross \: multiplying ;\\\\\sf \implies 11x + 4 = 70\\\\\sf \implies 11x = 70 - 4 \\\\\implies \sf 11x = 66\\\\\sf \implies x = \frac{66}{11}\\\\\sf \implies x = 6$

Hence, the value of x is 6.

_______________________

$\large{\underline{\underline{\mathfrak{\heartsuit \: Extra \: Information: \: \heartsuit}}}}$

What is Mean?

The average of a given set of numbers is called the Arithmetic mean, or simply the mean, of the given numbers.

Mean = $\sf \dfrac{Sum \: of \: observations }{Number \: of \: observations }$

Answer 2

Answer :-

x = 6

Solution :-

Given that

Observations = (2x + 3), (3x + 4), (x + 7), (x - 3), (4x - 7)

No. of observations = 5

Mean of observations = 14

$\boxed{ \sf Mean \: of \: observations = \dfrac{Sum \: of \: observations}{No. \: of \: observations} }$

$\tt \implies 14 = \dfrac{(2x + 3) + (3x + 4) + (x + 7) + (x - 3) + (4x - 7)}{5}$

$\tt \implies 14 = \dfrac{2x + 3 + 3x + 4 + x + 7 + x - 3 + 4x - 7}{5}$

$\tt \implies 14 = \dfrac{11x + 3 + 4 + 7 - 3 - 7}{5}$

$\tt \implies 14 = \dfrac{11x + 7 + 7- 3 - 7}{5}$

$\tt \implies 14 = \dfrac{11x + 7 - 3 }{5}$

$\tt \implies 14 = \dfrac{11x + 4}{5}$

By cross multiplication

$\tt \implies 14(5)= 11x + 4$

$\tt \implies 70= 11x + 4$

$\tt \implies 70 - 4= 11x$

$\tt \implies 66= 11x$

$\tt \implies \dfrac{66}{11} = x$

$\tt \implies x = 6$

$\tt \therefore \: x = 6$