Question

the denominator of a fraction is greater than the numerator by 8 if the numerator is increased by 17 and denominator is decreased by 1, the fraction obtained is 3 /2 . find the fraction I need

Answer 1

Let the numerator be x

Denominator is 8 more than numerator

So, let the denominator be x + 8

If the numerator increased by 17 = x + 17

If the denominator decreased by 1 = x + 8 - 1 = x + 7

The fraction obtained is $\dfrac{3}{2}$

According to the question,

$\dfrac{x + 17}{x + 8 - 1} = \dfrac{3}{2}$

➾ $\dfrac{x + 17}{x + 7} = \dfrac{3}{2}$

➾ $2(x\:+\:17)\:=\:3(x\:+\:7)$

➾ $2x\:+\:34\:=\:3x\:+\:21$

➾ $3x\:-\:2x\:=\:34\:-\:21$

➾ $x\:=\:13$

∴ The required fraction ➾ $\dfrac{x}{x + 8}$

➾ $\dfrac{13}{13 + 8}$

➾ $\large\boxed{\large\boxed{\large\boxed{\frac{13}{21}}}}}$

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Answer 2

here is your solution ☺☺☺☺☺☺

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Let the numerator be x

and the denominator is x+8

The fraction = x/x+8

Numerator is increased by 17 and the denominator is decreased by 1.

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
13 = x

fraction = x/x+8
=
13/13+8 = 13/21