Chapter 2.4, Problem 15E

Marriage Trends It is found that the number of married and single adults in a certain town are subject to the statistics that follow. Suppose that x and y denote the number of married and single adults, respectively, in a given year (say, as of January 1) and let m and s denote the corresponding numbers for the following year. Then,

$.8x+.3y=m$

$.2x+.7y=s$

(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, in a given year, there were found to be 100,000 married adults and 50,000 single adults. How many married and single adults were there the preceding year?

(d) How many married and single adults were there two years ago?