Question

The ratio of the numerator to the denominator of a fraction is 2 to 3. If both the numerator and the denominator are increased by 2, the fraction becomes 3/4. What is the original fraction?

Which of the following systems of equations can be used to solve the problem?

Answer 1

The clues translate to

n/d = 2/3
(n+2)/(d+2) = 3/4

Solving this by cross multiplying both:

3n = 2d
3(d+2) = 4(n+2) => 3d + 6 = 4n + 8

then substituting d = 3/2 n in the second:

9/2n - 4n = 2 => 1/2 n = 2 => n = 4

if n=4 then d = 3/2*4 = 6.

So the original fraction was 4/6