Question

The numerator of a fraction is 5 less then its denominator. if twice the numerator is 1 more than the denominator, find the fraction.

Answer 1

Let the value of our numerator be a and the value of our denominator b. Then from the first condition we get that $a+5=b$, or $a-b=-5$.

From the second condition, we get that $2a=b+1$, or $2a-b=1$.

As both equations must be true, we have a following system of equations:

$\left \{ {{a-b=-5} \atop {2a-b=1}} \right.$.

To solve this, we multiply the 2nd equation by -1, which will yield us

$\left \{ {{a-b=-5} \atop {-2a+b=-1}} \right.$.

Adding the two equations together, we get that $-a=-6$, from which we get that $a=6$. Plugging it into the first equation we get that $-b=-11$, from which $b=11$. Thus, our final answer is $\frac{6}{11}$.

Answer 2

Simple and easy hope it helps