Question

2. Let’s pretend that in an American city there were 2000 new cases on Monday which is a 12% decrease from two weeks ago. So it appears that new covid cases are going down (wahoo!) with a two-week trend of -12%. How many new cases were there two weeks ago? (don’t round for accuracy)

Answer 1

Answer:

22

Explanation:

Let the number of new cases two weeks ago = x

After a decrease of 12%, the number of new cases on Monday = 2000.

So, we have that:

$\begin{gathered} x-12\%\text{ of x}=2000 \\ x-0.12x=2000 \end{gathered}$

The equation is then solved for x:

$\begin{gathered} 0.88x=2000 \\ \text{ Divide both sides by 0.88} \\ \frac{0.88x}{0.88}=\frac{2000}{0.88} \\ x=2000\div\frac{88}{100} \\ x=2000\times\frac{100}{88} \\ =2000\times\frac{25}{22} \\ x=2272\frac{8}{11} \end{gathered}$

There were approximately 2,273 new cases two weeks ago.