Covid Patients Average Recovery Days

Let $n$ be the number of patients admitted in hospital A. Then hospital B admitted $n + 21$ patients.

Average recovery days in A $= \frac{200}{n}$. Average recovery days in B $= \frac{152}{n + 21}$.

Given: $\frac{200}{n} - \frac{152}{n + 21} = 3$ $200(n + 21) - 152n = 3n(n + 21)$ $200n + 4200 - 152n = 3n^2 + 63n$ $48n + 4200 = 3n^2 + 63n$ $3n^2 + 15n - 4200 = 0$ $n^2 + 5n - 1400 = 0$ $(n + 40)(n - 35) = 0$

Since $n > 0$, $n = 35$. Hospital A admitted 35 patients.