Question

2. The denominator of a fraction is one less than twice its numerator. If the numerator is decreased by 3, it becomes 1/7. Find the fraction.​

Answer 1

Answer:

The fraction is $\frac{4}{7}$ .

Step-by-step explanation:

Let the numerator of the fraction be $x$ and the denominator be $y$.

Since the denominator is one less than twice the numerator, we have the equation,

$y=2x-1$

Also, if the numerator is decreased by 3, then the fraction equals $\frac{1}{7}$ . Thus,

$\dfrac{x-3}{2x-1}=\dfrac{1}{7}$

On solving the above equation,

$\implies (x-3)7=2x-1\\\\\implies 7x-21=2x-1\\\\\implies 7x-2x=-1+21\\\\\implies 5x=20\\\\\implies x=\frac{20}{5}=4$

So the numerator of the fraction is 4. The denominator is

$y=2x-1=2\times 4-1=8-1=7$

Hence the fraction is $\frac{4}{7}$ .