Question

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to 1/2.If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?5n = 3d and n - 2 = 2d - 45n = 3d and 2n - 4 = d - 23n = 5d and 2n - 4 = d - 2

Answer 1

We have a fraction, with a numerator and denominator.

We know that the numerator and denominator are in the ratio of 3 to 5, so we can write:

$\begin{gathered} \frac{n}{d}=\frac{3}{5} \\ 5n=3d \end{gathered}$

We also know that when we substract 2 from the numerator and also from the denominator, we obtain 1/2.

We can write and rearrange this as:

$\begin{gathered} \frac{n-2}{d-2}=\frac{1}{2} \\ 2(n-2)=1\cdot(d-2) \\ 2n-4=d-2 \end{gathered}$

Then, we can write the two equations as:

$\begin{cases}5n=3d \\ 2n-4=d-2\end{cases}$

Answer: 5n = 3d and 2n - 4 = d - 2 [Second option]