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 obtained is 3/2. Find the rational
number.​

Answer 1

AnswEr:

Let us Consider that the Number be x.

According to Question,

Denominator is Greater than the Numerator by 8.

So, Denominator = x + 8.

Number = $\sf\dfrac{x}{x+8}$

If the Numerator is increased by 17 & the denominator is decreased by 1, Number obtained is $\sf\dfrac{3}{2}$ [Given]

Therefore,

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

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

$\:\:\:\:\:\:\;\:\:\:\:\:\:\;\dag\:\:\footnotesize\bold{\underline{\underline{\sf{\red{Cross\: Multiplying}}}}}$

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

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

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

$\implies\sf\: 3x = 2x + 13$

$\implies\sf\: 3x - 2x = 13$

$\implies\large\boxed{\sf{\purple{ x\:=\:13}}}$

Now, Finding Number

$\implies\sf\: \dfrac{x}{x + 8}$

$\implies\sf\: \dfrac{13}{13 + 8}$

$\implies\sf\: \dfrac{13}{21}$

Hence, Required Number is $\sf\dfrac{13}{21}.$

$\rule{250}2$

Answer 2

$\huge \mathfrak \red{answer}$

__________________________________

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 obtained is 3/2. Find the rational

number.

_________________________________

step to step explanation:

$⇒\rm \blue{numerator \: be \: x}$

$⇒ \rm{denominator \: is \: x + 8}$

Given from question

__________________________

then

$\rm \red{ \frac{x}{x + 8}}$

then

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

from the question

$⇒ \tt{ \frac{x + 17}{x} + 8 - 1}$

$\tt{ = \frac{3}{2}}$

$\tt{⇒ \frac{x + 17}{x + 7} = \frac{3}{2}}$

then now cross multiplying

$\tt{⇒3(x + 7) = 2(x + 17)}$

$\tt{⇒3x + 21 = 2x + 34}$

$\tt{⇒3x - 2x = 34 - 21}$

$\tt{⇒x = 13}$

then now,

$\bf{x = 13}$

$\bf{x + 8}$

fraction:

$\bf{⇒ \frac{x}{x + 8}}$

$\bf{⇒ \frac{13}{13 + 8}}$

$\bf{⇒ \frac{13}{21}}$

so Answer is

$\bf \red{⇒ \frac{13}{21}}$

I hope it's help uh

the rational will be

$\sf{ \frac{13}{21}}$

____________________________

what is rational number?

• any number can be expressed that can be expressed as a fraction a/b

• where a and b are both integer ,but b can't be zero

I hope it's help uh