Question

The sum of the numerator and denominator of the fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.

Answer 1

Let the fraction be x/y.

We know that x + y = 12, and that (x) / (y + 3) = 12.

Multiplying both sides of the second equation by (y + 3), we get:

x = 12(y + 3)

Substituting this into the first equation, we get:

12(y + 3) + y = 12

Expanding and simplifying, we get:

13y + 36 = 12

Subtracting 36 from both sides, we get:

13y = -24

Dividing both sides by 13, we get:

y = -24/13

Substituting this value of y into the equation x + y = 12, we get:

x - 24/13 = 12

Multiplying both sides by 13, we get:

13x - 24 = 156

Adding 24 to both sides, we get:

13x = 180

Dividing both sides by 13, we get:

x = 180/13

Therefore, the fraction is 180/13 divided by -24/13, which simplifies to -15/2.