Question

Please answer it ..





........

Answer 1

$<h3>REFER to the attached picture. </h3>$

Answer 2

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

Given,
$\textit{Statement-1:}$
The Denominator of a rational number is greater than its numerator by 8

$\textit{Statement-2:}$
If Numerator is increased by 17 and the denominator is decreased by 1 the number obtained is $\dfrac{3}{2}$

$\sf\textsf{Rational Number = ?}$



$\underline{\Large{\textsf{Step-1:}}}$
$\sf\textsf{Assume variables for Numerator}\\\sf\textsf{and Denominator}$

$\sf\textsf{Let \textbf{p} be the Numerator}\\\sf\textsf{and \textbf{q} be the Denominator}$



$\underline{\Large{\textsf{Step-2:}}}$
$\sf\textsf{Express the Rational Number} \\ \sf \textsf{in terms of these variables.}$

$\sf\textsf{Rational Number = \dfrac{p}{q} }$ ———[1]



$\underline{\Large{\textsf{Step-3:}}}$
$\sf\textsf{Rewrite Statement-1}$

$\implies \textsf{q = p+8}$ ———[2]



$\underline{\Large{\textsf{Step-4:}}}$
$\sf\textsf{Rewrite Statement-2}$

$\implies\dfrac{p+17}{q-1}=\dfrac{3}{2}$ ———[3]



$\underline{\Large{\textsf{Step-5:}}}$
Substitute [2] in [3]

$\implies \dfrac{p+17}{(p+8)-1} = \dfrac{3}{2} }$



$\underline{\Large{\textsf{Step-6:}}}$
$\sf\textsf{Cross Multiply and simplify}\\\sf\textsf{obtain value of a variable.}$

$\begin{aligned} \implies 2(p+17) &= 3[(p+8)-1] \\ \implies 2p+34 &= 3(p+7) \\ \implies 2p+34 &= 3p+21 \\ \implies 3p-2p &= 34-21 \\ \implies p &= 13 \end{aligned}$



$\underline{\Large{\textsf{Step-7:}}}$
$\sf\textsf{plug in 13 for p in [2] to get}\\\sf\textsf{value of other variable.}$

$\begin{aligned} \implies q &= 13 + 8 \\ \implies q&=21 \\ \end{aligned}$


$\underline{\Large{\textsf{Step-8:}}}$
$\sf\textsf{Substitute p and q in [1]}$

$\sf\textsf{Rational Number = \dfrac{13}{21} }$


$\blacksquare\: \: \: \textsf{The Required Rational Number = \Large{\textbf{ \dfrac{13}{21} }}}$