Question

the denominator of the fraction is 3 more than the numerator. if 5 is added to both parts, the resulting fraction is equivalent to 4 by 5. find the fraction.​

Answer 1

Answer:

numerator is 3 morethan denominator

so fraction is x/(x+3)

adding 5 to both num and den

gives =>

(x+5)/(x+8) = 4/5

cross multiplying =>

(x+5)5 = (x+8)4

5x-4x = 32-25

x = 7

so required fraction is ,

7/7+3. = 7/10

Answer 2

$\large \underline{\pmb{\mathfrak{Given....}}}$

Given that, the denominator of a fraction is 3 more than the numerator. If 5 is added to both parts, the resultant fraction is equivalent to $\sf \dfrac{4}{5}.$

$\large\underline {\pmb{\frak{To~ find....}}}$

We have to find the fraction.

$\large\underline{\pmb{\frak{Solution....}}}$

❍ According to the question :

The denominator of the fraction is 3 more than the numerator, let :

$\qquad \sf ➠~Numerator~ =~ x$

$\qquad \sf➠~ Denominator ~=~ x+3$

So, the fraction will be :

$\qquad \sf ➠~Fraction ~=~ \dfrac{x}{x+3}$

❍ Also, if 5 is added to both the parts, the fraction will $\sf\dfrac{4}{5}$ :

$\qquad \sf ➠~\dfrac{x+5}{(x+3)+5}~=~ \dfrac{4}{5}$

$\qquad \sf ➠~\dfrac{x+5}{x+8}~=~\dfrac{4}{5}$

❍ Cross multiplying them :

$\qquad \sf➠ ~5(x + 5 )= 4(x + 8)$

$\qquad \sf ➠~5x + 25 = 4x + 32$

$\qquad \sf➠ ~5x - 4x + 25 - 32 = 0$

$\qquad \sf ➠~x - 7 = 0$

$\qquad \sf➠ ~x = 7$

❍ Substituting the value of x in the fraction :

$\qquad \sf ➠~Fraction = \dfrac{x}{x + 3}$

$\qquad \sf ➠~Fraction = \dfrac{7}{7 + 3}$

$\qquad \sf ➠~Fraction = \dfrac{7}{10}$

_________________________

❍ Therefore, the fraction is $\bf\dfrac{7}{10}.$