Question

the denominator of a rational number is greater than its numerator by 8 if the numerator is increased by 17 and the denominator is decreased by 1 the number update is 3 upon 2 find the rational number​

Answer 1

Step-by-step explanation:

here is your answer and once try to solve it yourself

Answer 2

Given :

• The denominator of a rational number is greater than its numerator by 8
• If the numerator is increased by 17 and the denominator is decreased by 1 the number obtained is 3/2

To Find :

• The Rational Number

Solution :

Let the numerator be x.

Let the denominator be y.

Rational Number = $\sf{\dfrac{x}{y}}$

Case 1 :

The denominator, y is is greater than numerator, x by 8.

Equation :

$\bold{y=x+8\:\:\:(1)}$

Case 2 :

The numerator when is increased by 17 and denominator decreased by 1, the rational number then is 3/2.

Numerator = (x + 17)

Denominator = (y-1)

Equation :

$\longrightarrow$ $\bold{\dfrac{x+17}{y-1}=\dfrac{3}{2}}$

$\longrightarrow$ $\bold{2(x+17)=3(y-1) }$

$\longrightarrow$ $\bold{2x+34=3y-3}$

$\longrightarrow$ $\bold{2x-3y=-3-34}$

$\longrightarrow$ $\bold{2x-3y=-37}$

From equation (1), y = x + 8,

$\longrightarrow$ $\bold{2x-3(x+8)=-37}$

$\longrightarrow$ $\bold{2x-3x-24=-37}$

$\longrightarrow$ $\bold{-x=-37+24}$

$\longrightarrow$ $\bold{\cancel{-}x=\cancel{-}13}$

$\longrightarrow$ $\bold{x=13}$

Substitute, x = 13 in equation (1),

$\longrightarrow$ $\bold{y=x+8}$

$\longrightarrow$ $\bold{y=13+8}$

$\longrightarrow$ $\bold{y=21}$

$\large{\boxed{\bold{Numerator\:=\:x\:=\:13}}}$

$\large{\boxed{\bold{Denominator\:=\:y\:=\:21}}}$

$\large{\boxed{\bold{Rational\:Number\:=\:\dfrac{x}{y}\:=\:\dfrac{13}{21}}}}$