Question

50 POINTS

The denominator of a fraction is 10 more than its numerator.

When 1/3 is added to this fraction, the resulting fraction’s denominator is three times the denominator of the original fraction its numerator is 15 less than its denominator.

What is the numerator of the original fraction?

Answer 1

5

Explanation:

Let us assume that x is the numerator of the original fraction. Then the denominator of the original fraction is (x + 10).

When we add
`(1)/(3)` to the original fraction then it becomes a new fraction.

And the new fraction is
`(x)/(x + 10) + (1)/(3) = (4x + 10)/(3(x + 10))`

Now, the numerator of the new fraction is 15 less than its denominator.

Hence, 4x + 10 + 15 = 3(x + 10)

⇒ 4x + 25 = 3x + 30

⇒ x = 5 (Answer)