Question

The denaminator of a rational number is greater than it's numerator by 8.It numerator is inereased by 17 and the denaminator is dvereased by the number original is 3 /2 find the rational number

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Answer 1

Given :-

• The denominator of a rational number is greater than it's numerator by 8.

• If numerator is increased by 17 and the denominator is decreased by 1 the number original is 3/2.

To find:

• The rational number?

Solution:

☯ Let the numerator of the rational number be x.

☯ Then, the denominator will be x + 8.

Therefore,

The rational number will be x/(x + 8)

★ According to the Question:

➵ (x + 17)/((x + 8) - 1) = 3/2

➵ (x + 17)/(x + 7) = 3/2

➵ 2(x + 17) = 3(x + 7)

➵ 2x + 34 = 3x + 21

➵ 34 − 21 = 3x − 2x

➵ x = 13

Therefore,

• Numerator of the rational number, x = 13
• Denominator of the rational number, x + 8 = 13 + 8 = 21

∴ Hence, The required rational number is 13/21.

Answer 2

Answer :

$\underline{\red{\frak{ \quad Given : \quad}}}$

• The denominator of a rational number is greater than it's numerator by 8.If numerator is increased by 17 and the denomintaor is decreased by the number original is 3/2.

$\underline{\red{\frak{ \quad To\:Find : \quad}}}$

$\bullet \: \: \textsf{Rational Number = ?}$

$\underline{\red{\frak{ \quad Solution : \quad}}}$

Let Numerator be x.

It is given that, The denominator of a rational number is greater than it's numerator by 8 :

Therefore, Denominator = x + 8

So, our rational number becomes :

$\sf \dfrac{Numerator}{Denominator} = \dfrac{x}{x + 8}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

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

$:\implies \sf \dfrac{x + 17}{x + 7} = \dfrac{3}{2}$

$\qquad \quad\small\underline{\frak{By \: Cross \: multiplying \: both \: the \: sides \: we \: get :}}$

$:\implies \sf (x + 17)2= 3(x + 7)$

$:\implies \sf 2x + 34= 3x + 21$

$\qquad \quad\small\underline{\frak{By \: combining \: like \: terms \: we \: get :}}$

$:\implies \sf 34 - 21 = 3x - 2x$

$:\implies \sf 34 - 21 = x$

$:\implies \sf x = 13$

$\large\bigstar \: \: \underline{\textsf{Required rational number :}}$

$\dashrightarrow\:\:\sf Required \: rational \: number = \dfrac{Numerator}{Denominator}$

$\dashrightarrow\:\:\sf Required \: rational \: number = \dfrac{x}{x + 8}$

$\dashrightarrow\:\:\sf Required \: rational \: number = \dfrac{13}{13 + 8}$

$\dashrightarrow\:\: \underline{ \boxed{\textsf{\textbf{Required rational number = \dfrac{\text{13}}{\text{21}} }}}}$

$\therefore\:\underline{\textsf{The required rational number is \textbf{ \dfrac{\text {13}}{\text {21}} }}}.$