Question

Which of the following is the solution to the equation $\frac{4}{5}n=20$?

• A. $\begin{array}{rcl}n& =& 4\end{array}$
• B. $\begin{array}{rcl}n& =& 12\end{array}$
• C. $n\begin{array}{rcl}& =& \end{array}\begin{array}{rcl}& & 16\end{array}$
• D. $\begin{array}{rcl}n& =& 25\end{array}$

Answer 1

The correct option is D

$\begin{array}{rcl}n& =& 25\end{array}$

Explaining the correct answer:

• The given equation is $\frac{4}{5}n=20$
• Now simplifying the equation.
• Multiply by $\frac{5}{4}$on both sides:

$\begin{array}{rcl}\frac{4}{5}n\times \frac{5}{4}& =& 20\times \frac{5}{4}\\ & \Rightarrow & n=5\times 5\\ & \Rightarrow & n=25\end{array}$

• Since the obtained value is the same as the option $\left(C\right)$ and the solution has a unique answer.
• Thus, the other options (option $\left(A\right)$, option $\left(B\right)$, and option $\left(D\right)$ are incorrect.

Hence, the option $\left(D\right)$ is the correct option.