select the correct answer.\nthe time it takes to clean up after an anniversary party varies inversely as the…

Explanation:

Step1: Establish inverse - variation formula

Let $t$ be the time and $n$ be the number of people. The inverse - variation formula is $t=\frac{k}{n}$, where $k$ is a constant. When $n = 3$ and $t=90$, we can find $k$. Substitute into the formula: $90=\frac{k}{3}$.

Step2: Solve for the constant $k$

Multiply both sides of the equation $90=\frac{k}{3}$ by 3. We get $k = 90\times3=270$.

Step3: Find the new time

Now, we want to find $t$ when $n = 5$. Substitute $k = 270$ and $n = 5$ into the formula $t=\frac{k}{n}$. So $t=\frac{270}{5}=54$.

Answer:

A. 54 minutes