Question

The numerator and denominator of a fraction are in the ratio of 1 to 3. If the numerator and denominator are bothincreased by 2, the fraction is now equal to 3/4. If n= the numerator and d= the denominator, which of the following systems of equations could be used to solve theproblem?3n= d and 4n+ 8 = 30 + 63n= d and 4n+ 6 = 30 + 5on=3d and 3n+ 6 = 20 + 4On=3d and 3n+ 6 = 40 + 8

Answer 1

Consider that 'n' is the numerator, and 'd' is the denominator of the fraction.

Given that the ratio of numerator to denominator is 1 to 3,

`\begin{gathered} (n)/(d)=(1)/(3) \\ \Rightarrow d=3n \end{gathered}`

Given that if the numerator and denominator are both increased by 2, the fraction is now equal to 3/4,

`\begin{gathered} (n+2)/(d+2)=(3)/(4) \\ 4(n+2)=3(d+2) \\ 4n+8=3d+6 \end{gathered}`

Thus, the required system of equations is,

`\begin{gathered} d=3n \\ 4n+8=3d+6 \end{gathered}`

Therefore, first option is the correct choice.