Chapter 2.4, Problem 16E

Epidemiology A flu epidemic is spreading through a town of 48,000 people. It is found that, if x and y denote the numbers of people sick and well in a given week, respectively, and if s and w denote the corresponding numbers for the following week, then

$\frac{1}{3}x+\frac{1}{4}y=s$

$\frac{2}{3}x+\frac{3}{4}y=w$

(a) Write this system of equations in matrix form.

(b) Solve the resulting matrix equation for $X=\left[\begin{array}{c}x\\ y\end{array}\right]$.

(c) Suppose that 13,000 people are sick in a given week. How many were sick the preceding week?

(d) Same question as part (c), except assume that 14,000 are sick.