Answer: The correct option is
(A) [tex]5n=3d~~~\textup{and}~~~3n+6=2d+4.[/tex]
Step-by-step explanation: Given that the numerator and denominator of a fraction are in the ratio of 3 to 5. When the numerator and denominator are both increased by 2, the fraction is equal to \dfrac{2}{3}.
We are to select the system of equations that could be used to solve the problem.
Since n denotes the numerator and m denotes the denominator of the given fraction, so we have
[tex]\dfrac{n}{d}=\dfrac{3}{5}\\\\\\\Rightarrow 5n=3d,[/tex]
and
[tex]\dfrac{n+2}{d+2}=\dfrac{2}{3}\\\\\\\Rightarrow 3(n+2)=2(d+2)\\\\\Rightarrow 3n+6=2d+4.[/tex]
Thus, the required system of equations is
[tex]5n=3d~~~\textup{and}~~~3n+6=2d+4.[/tex]
Option (A) is CORRECT.
