Question

Anupa's favorite fraction is equivalent to $\frac{3}{5}$. The sum of its numerator and denominator is $120$. What is the difference between the denominator and numerator of Anupa's favorite fraction?

Answer 1

Let Anupa's favorite fraction be $\frac{x}{y}$.

Since it is equivalent to $\frac{3}{5}$, clearly x < y.

It is give that the sum of the numerator and the denominator is $120$.

Therefore, x + y = 120 --- (1)

We need to find y - x.

Now, from (1),

y = 120 - x

So, $\frac{x}{120-x} =\frac{3}{5}$

5x = 3(120 - x)

= 360 - 3x

5x + 3x = 360

8x = 360

x = 360/8

= 45

y = 120 - 45 = 75

y - x = 75 - 45 = 30

Hence, the difference between the denominator and numerator of Anupa's favorite fraction is 30.