# The denominator of a fraction is 4 more than twice the numerator. Determine the fraction.

The denominator of a fraction is $4$ more than twice the numerator. When both the numerator and denominator are decreased by $6$, the denominator becomes $12$ times the numerator. Determine the fraction.

I tried the following,

Let the numerator be $x$ and the denominator be $y$

Therefore, Fraction$=$ $x$/$4$$+$$2$$x Because, both the numerator and denominator are decreased by 6 Therefore, the new fraction becomes x$$-$6/$($$4$$+$$2$$x$$)$$-$$6$$=$$12$$x$

I do not know how to proceed further.

• I think your last equation isn't right. Shouldn't it be $4+2x-6 = 12\cdot(x-6)$? I think the statement refers to the numerator and denominator of the modified fraction, doesn't it? – MPW Jul 29 '14 at 17:06
• "$y$ is $4$ more than twice $x$" translates to $y=4+2x$. So the fraction is $x/y=x/(4+2x)$, which is hardly the same as $x/4+2x$. – blue Jul 29 '14 at 17:09

$$y=2x+4$$

$$12(x-6)=y-6$$
Because if the denominator is 12 times the numerator that means that your fraction is equal to $\frac{1}{12}$.
So from this system of equations you can get the values of $x$ and $y$. I will give them to you but I'll let you go through the last steps of the process to get them:
$$x=7 \qquad y=18$$