Question

the denominator of a certain fraction is 5 more than the numerator, if 3 is added to both terms of the fraction, the resulting fraction equals 1/2. find the fraction.

Answer 1

x/x+5
x+3/x+8 = 1/2
cross multiply and equate :3

Answer 2

$\underline{\textbf{Hey Mate Here Is Your Answer }}$

$\underline{\bold{Given\: That...}}$

The Denominator Of A Certain Fraction Is 5 More Than The Numerator, If 3 Is Added To Both Terms Of The Fraction, The Resulting Fraction Equals 1/2, Now We Need To Find The The Fraction ..

So Now Let's Move For Solution..

$\underline{\bold{Solution..}}$

So now To Find The Fraction Follow The Simple Steps .

$\underline{\bold{Step-1\:) \:D e f i n e\: All\: The\: Required\: Terms \: With\:Help\: Of \: Variables}}$

So Now Let ..

$\textbf{Numerator = X }$

Therefore Now According To Question Denominator Is 5 More

Than Numerator Therefore We Have...

$\textbf{Denominator = Numerator + 5 }$

That Is

$\textbf{Denominator = X + 5 }$

So The Obtained Fraction Form Is

$\boxed{\mathbf{\frac{x}{x+5} }}$

$\underline{\textbf{Step-2 ) Form An Equation With The Help of Information Given In Question}}$

So According To Question ...

If 3 Is Added To Both Numerator And Denominator Then It Will Be Equal To $\frac{1}{2}$

So By This We Have

$\boxed{\mathbf{\frac{(x) \:+\: 3}{(x\: + \:5)+\: 3} = \frac{1}{2}}}$

$\underline{\textbf{Step-3 ) Solve The Equation ...}}$

So We Have ....

$\large{\mathbf{\frac{(x) \:+ \:3}{(x\: + \:5 )+ 3} = \frac{1}{2}}}$

That Is ..

$\large{\mathbf{\frac{x\: + \:3}{x + \:8} = \frac{1}{2}} }$

Now Cross Multiplying LHS And RHS ...

We Have ...

$\mathbf{2(x + 3) \: = \: 1(x + 8)}$

That Is ...

$\mathbf{2x + 6 = x + 8}$

Now Taking 6 To RHS And Taking X To LHS We Have...

$\mathbf{2x - x = 8 - 6}$

That Is ...

$\textbf{x = 2}$

Therefore We Have Value Of

$\boxed{\bold{x\:=\:2}}$

$\underline{\textbf{Step-4 ) Put The Value Of X In The Assumed Fraction Form}}$

So That Is ..

$\textbf{Numerator = X => 2 }$

And

$\textbf{Denominator = X + 5 =⇒ 2 + 5 = 7 }$

Therefore The Required Fraction Is ...

$\boxed{\mathbf{\frac{2}{7} }}$

$\underline{\textbf{Hence The Required Answer Is ..}}$

$\boxed{\bold{\frac{2}{7}\: - \: Answer}}$

$\large{\bold{Thanks...}}$