1. A product is made by only two competing companies. Suppose Company X retains two-thirds of its customers and loses one-third to Company Y each year, and Company Y retains three quarters of its customers and loses one-quarter to Company X each year. We can represent the number of customers each company had last year by

Where x0 is the number Company X had and y0 is the number Company Y had. Then the number that each will have this year can be represented by

If Company X has 1900 customers and Company Y has 1700 customers this year, how many customers did each have last year?
2. Suppose that a government study showed that 90% of urban families remained in an urban area in the next generation (and 10% moved to a rural area), whereas 70% of rural families remained in a rural area in the next generation (and 30% moved to an urban area). This means that if

Represents the current percents of urban families, u0, and of rural families, r0, then

represents the percents of urban families, u, and rural families, r, one generation from now. Currently the population is 60% urban and 40% rural. Find the percents in each group one generation before this one?

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