Question

Adding 6 to numerator of a fraction , the numerator becomes twice the denominator. Write the equation(s) that represent the given statement.

Answer 1

Let numerator of the fraction be $x$ and denominator be $y$ i.e. the fraction is $\frac{x}{y}$.

Adding 6 to numerator i.e. $(x+6)$ , the numerator becomes twice the denominator.
$\Rightarrow (x+6=2y)$

Similarly, we can assume numerator of the fraction be $y$ and denominator be $x$.
If we interchange the variables used for the numerator and denominator as $y$ and $x$ respectively (i.e. the fraction is $\frac{y}{x}$), then the equation is $y+6=2x$.

Hence, x + 6 = 2y and y + 6 = 2x represent the given statement.