Question

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

Accepted Answer

35. 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.

Covid Patients Average Recovery Days

Explanation

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