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.

  • $\begingroup$ 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? $\endgroup$ – MPW Jul 29 '14 at 17:06
  • 1
    $\begingroup$ "$y$ 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 $x/4+2x$. $\endgroup$ – blue Jul 29 '14 at 17:09

Using your notation you have:


And the next condition reads:


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:

$$x=7 \qquad y=18$$


let the numerator be x and let the denominator be y... in the first part of the question it is said that,x/2x*4(*is plus).in second part of the question it is said that : x-6/(2x*4)-6.now finally at the last part of the question it is said that: 2x-2=12x[x-6] 2x-2=12x-72 2x-12x= -72+2 -10x=-70 x=7... in first part of the question we saw that...y=2x+4...now substitute the value of x in that....you get 2.7+4=18...therefore the required fraction is 7/18....hope u understand...[• indicates multiplication]

  • $\begingroup$ useful.clear. good $\endgroup$ – user351943 Jul 4 '16 at 11:52

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