Question

If the average of 39, 48,51, 63, 65, 83, X and 69 is 60 then the value of x will be​

Answer 1

$\sf\Large{\underline{\underline{Answer:-}}}$

The value of x is 32.

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$\sf\Large{\underline{\underline{Explaination:-}}}$

★ Given,

• Average of 39, 48,51, 63, 65, 83, x and 69 is 60
• Number of terms = 8

⠀

$\sf\Large{\underline{\underline{To \: Find :-}}}$

• The value of x

⠀

$\sf\Large{\underline{\underline{Formula \: to \: be \: used :- }}}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;average\;=\;\bf{{ \frac{sum \: of \: all \: terms}{number \: of \: terms_{(addends)}} }\:}}\end{gathered}$

⠀

$\sf\Large{\underline{\underline{Solution:-}}}$

We are said that the average of 39, 48,51, 63, 65, 83, x and 69 is 60. find the value of x in it.

To find the value of x , insert the values in the Formula of Average and solve for the variable 'x'. Let's find it !

⠀

• Average (given) = 60
• Number of terms = 8

$\begin{gathered}\\\;\sf{:\rightarrow\;\;60\;=\;\bf{{\dfrac{39 + 48 + 51 + 63 + 65 + 83 + x + 69}{8} }\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;60\;=\;\bf{{\dfrac{448 + x}{8} }\:}}\end{gathered}$

• Sum of all terms is (448 + x)

• Transposing R.H.S (8) to L.H.S. (multiplication) –

$\begin{gathered}\\\;\sf{:\rightarrow\;\;60 \times 8\;=\;\bf{{{448 + x}}\:}}\end{gathered}$

• Solving the L.H.S.

$\begin{gathered}\\\;\sf{:\rightarrow\;\;480\;=\;\bf{{{448 + x}}\:}}\end{gathered}$

• Again, Transposing R.H.S. (448) to L.H.S. (subtraction)–

$\begin{gathered}\\\;\sf{:\rightarrow\;\;480 - 448\;=\;\bf{{{ x}}\:}}\end{gathered}$

• By subtraction,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;32\;=\;\bf{{{ x}}\:}}\end{gathered}$

${\underline{\underline{\sf{\green{The \: value \: of \: x \: is \: 32}}}}}$

⠀

ᴠᴇʀɪғɪᴄᴀᴛɪᴏɴ:-

To verify, substitute the obtained value in the Formula.

Here,

• Sum of all terms = 448 + x
• Value of x = 32
• Average = 60

$\begin{gathered}\\\;\sf{:\rightarrow\;\;60\;=\;\bf{{\dfrac{448 + 32}{8} }\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;60\;=\;\bf{{\dfrac{480}{8} }\:}}\end{gathered}$

• On Cancellation, we get

$\begin{gathered}\\\;\sf{:\rightarrow\;\;60=\;\bf{{ \sf{\cancel\dfrac{480}{8}}}\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;60\;=\;\bf{{60 }\:}}\end{gathered}$

As, R.H.S = L.H.S

So, the obtained value of x i.e., 32 is correct.