Question

When the numerator is increased by 17 and the denominator is decreased by 1, the fraction obtained is $\frac{3}{2}$. Knowing that the denominator is greater than the numerator by 8, how do we represent the above situation in the form of an equation?

• A. $\frac{N+7}{N+17}=\frac{3}{2}$
• B. $\frac{N+17}{N+7}=\frac{3}{2}$
• C. $\frac{N+17}{N+7}=\frac{2}{3}$
• D. $\frac{N+7}{N+17}=\frac{2}{3}$

Answer 1

The correct option is B $\frac{N+17}{N+7}=\frac{3}{2}$

We know that the denominator is greater than numerator by 8.
Hence, D = N + 8.

Now, when denominator is decreased by 1, the expression becomes
D - 1 = N + 8 - 1 = N + 7.

Now, when the numerator is increased by 17, the expression will be N+17.

Hence, the new fraction obtained will be $\frac{N+17}{N+7}$.

We know that the fraction obtained is equal to $\frac{3}{2}$.

Hence $\frac{N+17}{N+7}=\frac{3}{2}$.