Question

*What should be the value of x so that the average of the numbers 2,x,3,5,7 is 4 ?*

1️⃣ 4
2️⃣ 5
3️⃣ 3
4️⃣ 1
​

Answer 1

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{GIVEN:-}$

The average of the numbers 2 , x , 3 , 5 , 7 is 4.

$\underline \mathbb{TO \: FIND:-}$

The value of x.

$\underline \mathbb{FORMULA:-}$

$Average \: = \: \frac{Sum \: of \: all \: the \: numbers}{ Total \: numbers}$

$\underline \mathbb{BY \: THE \: PROBLEM:-}$

$Average \: = \: \frac{Sum \: of \: all \: the \: numbers}{ Total \: numbers} \\ \\ \implies \: 4= \: \frac{2 + x + 3 + 5 + 7}{5} \\ \\ \implies \:4 \times 5 = 17 + x\\ \\ \implies \:20 = 17 + x\\ \\ \implies \:x = 20 - 17\\ \\ \implies \:x = 3$

$\underline \mathbb{ANSWER:-}$

$\implies \boxed{x = 3}$

$\underline \mathbb{VERIFICATION:-}$

$Average \: = \: \frac{Sum \: of \: all \: the \: numbers}{ Total \: numbers} \\ \\ \implies \:Average = \: \frac{2 + 3 + 3 + 5 + 7}{5} \\ \\ \implies \: \:Average = \frac{20}{5} \\ \\ \implies \: Average = 4(proved)$