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Question

A satellite company and a cable company compete for customers in a city. The satellite company retains 23\frac{2}{3} of its customers and loses 13\frac{1}{3} of its customers to the cable company, while the cable company retains 35\frac{3}{5} of its customers and loses 25\frac{2}{5} of its customers to the satellite company. If we represent the fraction of the market held last year by

[ab]\left[\begin{array}{l} a \\ b \end{array}\right]

where a is the number of customers that the satellite company had last year and b is the number that the cable company had last year, then the number that each company will have this year can be found by

[AB]=[23251335][ab]\left[\begin{array}{l} A \\ B \end{array}\right]=\left[\begin{array}{ll} \frac{2}{3} & \frac{2}{5} \\ \frac{1}{3} & \frac{3}{5} \end{array}\right]\left[\begin{array}{l} a \\ b \end{array}\right]

If the satellite company has A = 90,000 customers and the cable company has B = 85,000 customers this year, how many customers did each have last year?

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Answered 11 months ago
Answered 11 months ago
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In this task, we are interested in determining the number of customers each company had last year.

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