Question

the arithmetic mean. of 2x+3,3x+4,x+7,x-3and 4x-7is 14 find the Value of x​

Answer 1

Given :-

• The arithmetic mean of 2x+3, 3x+4, x+7, x+3 and 4x - 7 is 14

Aim :-

• To find the value of x

Answer :-

Concept applied :-

A number expressing the central or overall value of the given data is said to be the average/mean

Formula :-

$\boxed {\sf \longrightarrow \dfrac{sum \: of\: total \:number \:of\: observations}{total \: number \: of \: observations} }$

By substituting we get :-

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

Transposing 5, and removing the brackets,

$\implies \sf 2x + 3 + 3x + 4 + x + 7 + x - 3 + 4x - 7 = 14 \times 5$

Adding all the constants and the variables in the LHS (Left hand side of the equations) and multiplying in the RHS (Right hand side of the equation),

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

Transposing 4,

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

Subtracting,

$\implies \sf 11x = 66$

Transposing 11,

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

Reducing to the lowest terms,

$\implies \sf x = 6$

Therefore the value of x = 6

The numbers are :-

• 15 (2×6 + 3)
• 22 (3×6+4)
• 13 (6+7)
• 3 (6-3)
• 17 (4×6 - 7)

Verification :-

By finding the mean of these numbers, let us verify the answer.

Substituting,

$\implies \sf \dfrac{15 + 22+ 13 + 3 + 17}{5} = 14$

Solving LHS and RHS separately,

LHS :-

$\implies \sf \dfrac{70}{5}$

reducing to the lowest terms,

⇒ 14

RHS :-

⇒ 14

LHS = RHS

Hence verified.