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

Let the numerator be x, and the denominator be y. 

The ratio of the numerator to the denominator of a fraction is 2 to 3. 

>> x/y = 2/3 

If both the numerator and the denominator are increased by 2, the fraction becomes 3/4. 

>> (x + 2)/(y + 2) = 3/4 

From x/y = 2/3, x = (2/3)y 

From (x + 2)/(y + 2) = 3/4, cross multiply and we have 

4(x + 2) = 3(y + 2) 

Substitute x = (2/3)y into the equation above. 

4[(2/3)y + 2] = 3(y + 2) 

Distribute the lefh hand side and solve for y. 

(8/3)y + 8 = 3y + 6 

(8/3)y - 3y = 6 - 8 

-(1/3)y = -2 

y = 6 

x = (2/3)y = (2/3)(6) = 4 

Hence the numerator is 4, and the denominator is 6. 

Hope this helps!