Question

3 numbers have an average of 17. the first twowo numbers are 12 and 19. what i the third number?

Answer 1

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

➙ The third number is 20 ${\boxed{\green{\checkmark{}}}}$

${\blue{\underline{\underline{\purple{\textsf{\textbf{Step-by-step explanation: }}}}}}}$

Given that,

• 3 numbers average is 17.
• Out of the three numbers two of them are 12 & 19.

Here, two numbers out of the three is given we need to find the third number.

We know that,

${ \underline{ \boxed{ \sf average = \frac{sum \: of \: the \: numbers}{frequency \: of \: the \: number} }}}$

Here,

→ Average = 17

→ Sum of the numbers = 12 + 19 + x

• Assuming the third number as “x”

→ frequency of the numbers = 3

From the given values :

$\sf : \implies average = \frac{12 + 19 + x}{3}$

$\sf : \implies 17 = \frac{31 + x}{3}$

$\sf : \implies 17 \times 3 = 31 + x$

$\sf : \implies 51 = 31 + x$

$\sf : \implies 51 - 31 = x$

$\sf : \implies x = 20$

Therefore the third number is 20 ✔

Check point :

After solving we are getting three numbers as 12, 19 & 20. There average is 17 (given)

• To verify the third number as 20 find the average which must be equal to 17.

Again,

$\sf \to average = \frac{12 + 19 + x}{3}$

$\sf \to average = \frac{31 + x}{3}$

$\sf{[Substitute \: the \: value \: of \: x]}$

$\sf \to average = \frac{31 + 20}{3}$

$\sf \to average = \frac{51}{3}$

$\sf \to average = {17}$ ${\boxed{\green{\checkmark{}}}}$

• As we got the average 17 this means the third number is 20 ✔.

Answer 2

$\huge \mathfrak{ \color{skyblue}{A}} \mathfrak{ \color{pink}{n}} \mathfrak{ \color{skyblue}{s}} \mathfrak{ \color{pink}{w}} \mathfrak{ \color{skyblue}{e}}\mathfrak{ \color{pink}{r}}$

$\to$ The third number is 20.

$\large \sf{ \color{royalblue}{Step}} \sf{ \purple{-by-}} \sf{ \color{royalblue}{step}} \sf{ \purple{ \: explanation}}{ \color{royalblue}{ \: : }}$

Given that,

• 3 numbers average is 17.
• Out of the three numbers two of them are 12 & 19.

Here, two numbers out of the three is given we need to find the third number.

We know that :

${ \color{teal}{ \boxed{ \sf Average = \frac{Sum \: of \: the \: numbers}{ Frequency \: of \: the \: number}}}}$

Here,

→ Average = 17

→ Sum of the numbers = 12 + 19 + x

• Assuming the third number as “x”

→ Frequency of the numbers = 3

From the given values :

$\sf \implies average = \frac{12 + 19 + x}{3}$

$\sf \implies 17 = \frac{31 + x}{3}$

$\sf \implies 17 \times 3 = 31 + x$

$\sf \implies 51 = 31 + x$

${ \red{\sf \implies x = 20}}$

Therefore the third number is 20.

Check point :

• After solving we are getting three numbers as 12, 19 & 20. There average is 17 (given)

• To verify the third number as 20 find the average which must be equal to 17.

Again,

$\sf \longrightarrow average = \frac{12 + 19 + x}{3}$

$\sf \longrightarrow average = \frac{31 + x}{3}$

$\sf{(Substitute \: the \: value \: of \: x)}$

$\sf \longrightarrow average = \frac{31 + 20}{3}$

$\sf \longrightarrow average = \frac{51}{3}$

${ \red{\sf \longrightarrow average = {17}}}$

As we got the average 17 this means the third number is 20 .