Question

denominator of a fraction is 3 more than it's numerator . if the numerator is increased by 7 and the denominator is decreased by 2 , we obtain 2 . the sum of numerator and denominator of the fraction is ---

Answer 1

Hiii friend,

Let the denominator of the fraction be X.

Then the numerator of the fraction = (X-3)

Fraction = Numerator/Denominator = X-3/X.

Numerator and denominator are increased by 2 then the Numerator and denominator becomes (X-3+2) and (X+2).

Fraction = Numerator/Denominator =(X-3+2)/(X+2).

According to question,

(X-3+2)/(X+2) = 6/7

X-1/X+2 = 6/7

7(X-1) = 6(X+2)

7X-7 = 6X+12

7X-6X= 12+7

X = 19

Numerator = (X-3) = (19-3) = 16

And,

Denominator =(X) = 19

Therefore,

Original Fraction = Numerator/Denominator = (X-3)/X= 19/16

HOPE IT WILL HELP YOU.... :-)

Answer 2

$\textbf {Hey there, here is the solution.}$

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Define the fraction:

The denominator of a fraction is 3 more than its numerator.

Let the numerator be x.

$\text {The fraction is } \dfrac{x}{x + 3}$

.

Form equation and Solve x:

Numerator is increased by 7 and denominator decreased by 2, the result is 2:

$\dfrac{x+ 7}{x + 3 -2 } = 2$

$\dfrac{x + 7}{x + 1 } = 2$

$x + 7 = 2(x + 1)$

$x + 7 = 2x + 2$

$x = 5$

.

Find the fraction:

$\dfrac{x}{x + 3} = \dfrac{5}{5 + 3} = \dfrac{5}{8}$

.

Find the sum of the numerator and denominator of the fraction:

Sum = 5 + 8 = 13

.

Answer: The sum is 13.

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⭐$\textbf {Cheers @ Simmisai}$⭐