Question

9. Find a number such that when 5 is subtracted
from 5 times the number, the result is 4 more
than twice the number.

10. The numerator of a fraction is 5 less than its
denominator. If 3 is added to the numerator
and denominator both, the fraction becomes
. Find the original fraction.​

Answer 1

Answer:

9) x = 3

this is the answer

Answer 2

$\large \dag$ Question :-

The numerator of a fraction is 5 less than its denominator . If 3 is added to the numerator and denominator both , the fraction becomes 4/5 . Find the original fraction.

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{The   \: Original \:  Fraction  \: is \:  \frac{17}{22} }} }$

$\large \dag$ Step by step Explanation :-

Let Numerator and Denominator of Original Fraction be :

Numerator = x

As Per the question numerator of the fraction is 5 less than it's denominator so,

Denominator should be = x + 5

So ,

$\text{Original Fraction = } \frac{\text x}{\text x + 5}$

❒ When 3 is added to both the numerator and denominator :

$\\ \rm \text{Fraction Becomes } :  \frac{x +3}{x + 8}$

⏩ According To Question :

$\\ \large \blue \bigstar  \:   \red{ \bf  \frac{x+3}{x + 8} =  \frac{4}{5}  }$

$:\longmapsto \rm 5(x +3) = 4(x + 8)$

$:\longmapsto \rm 5x + 15 = 4x + 32$

$:\longmapsto \rm 5x - 4x = 32-15$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 17} }}}$

$\blue\dashrightarrow\underline{\underline{\sf  \orange{Numerator  \: of \:  Original  \: Fraction = 17 }} }$

☆ As numerator of the fraction is 5 less than it's denominator

$\rm\therefore \:  Denominator  = 17  + 5$

$\blue\dashrightarrow\underline{\underline{\sf  \orange{Denominator  \: of \:  Original  \: Fraction = 22}} }$

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{ Original  \: Fraction  =  \dfrac{17}{22} }}}}}$