Question

the denominator of a fraction is greater than its numerator by 2 if 4 is added to the numerator and 9 to
the denominator the new fraction is equivalent with 1 upon 2 find the fraction​

Answer 1

$\huge\underline{\textbf{Answer\::}}$

$\textbf{Let numerator be x and denominator}$ $\textbf{be y.}$

Now;

$\underline{A.T.Q.}$

The denominator of a fraction is greater than its numerator by 2.

y = x + 2 ___(1)

if 4 is added to the numerator and 9 to the denominator the new fraction is equivalent with 1 upon 2.

$\dfrac{x\:+\:4}{y\:+\:9}$ = $\dfrac{1}{2}$

Cross-multiply them

2(x + 4) = 1(y + 9)

2x + 8 = y + 9

2x - y + 8 - 9 = 0

2x - y - 1 = 0

2x - (x + 2) - 1 = 0 {From (1)}

2x - x - 2 - 1 = 0

x - 3 = 0

x = + 3

Put value of x in (1)

y = + 3 + 2

y = + 5

Fraction = $\dfrac{x}{y}$

=> $\dfrac{3}{5}$

Answer 2

Step-by-step explanation:

Let numerator be x and denominator \textbf{be y.}be y.

Now;

\underline{A.T.Q.}

A.T.Q.

The denominator of a fraction is greater than its numerator by 2.

y = x + 2 ___(1)

if 4 is added to the numerator and 9 to the denominator the new fraction is equivalent with 1 upon 2.

\dfrac{x\:+\:4}{y\:+\:9}

y+9

x+4

= \dfrac{1}{2}

2

1

Cross-multiply them

2(x + 4) = 1(y + 9)

2x + 8 = y + 9

2x - y + 8 - 9 = 0

2x - y - 1 = 0

2x - (x + 2) - 1 = 0 {From (1)}

2x - x - 2 - 1 = 0

x - 3 = 0

x = + 3

Put value of x in (1)

y = + 3 + 2

y = + 5

Fraction = \dfrac{x}{y}

y

x

=> \dfrac{3}{5}

5

3