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?
n + 4 = 3 and d + 5 = 4
3n - 2d = 0 and 4n + 2 = 3d + 2
3n = 2d and 4n + 8 = 3d + 6

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?
n + 4 = 3 and d + 5 = 4
3n - 2d = 0 and 4n + 2 = 3d + 2
3n = 2d and 4n + 8 = 3d + 6

parthkohli · Answer

$\Large \color{purple}{\rightarrow {2x + 2 \over 3x + 3} = {3 \over 4} }$

$\Large \color{purple}{\rightarrow 4(2x + 2) = 3(3x + 3) }$

$\Large \color{purple}{\rightarrow 8x + 8 = 9x + 9}$

$\Large \color{purple}{\rightarrow 8x = 9x + 1 }$

$\Large \color{purple}{\rightarrow x = -1 }$

anonymous · Answer

So you need 99 in engagement in order to graduate from high school?

anonymous · Answer

ParthKohli has the correct method.

Answer to the question is 3n - 2d = 0 and 4n + 2 = 3d + 2