At a certain university, three bookstores - the University Bookstore, the Campus Bookstore, and the Book Mart - currently serve the university community. From a survey conducted at the beginning of the fall quarter, it was found that the University Bookstore and the Campus Bookstore each had 40% of the market, whereas the Book Mart had 20% of the market. Each quarter the University Bookstore retains 80% of its customers, but loses 5% to the Campus Bookstore and 15% to the Book Mart. The Campus Bookstore retains 90% of its customers, but loses 5% to the University Bookstore and 5% to the Book Mart. The Book Mart retains 70% of its customers, but loses 5% to the University Bookstore and 25% to the Campus Bookstore.
If these trends continue, what percent of the market will each store have at the beginning of the second quarter? What percent of the market will each store have at the beginning of the third quarter?

Question

At a certain university, three bookstores - the University Bookstore, the Campus Bookstore, and the Book Mart - currently serve the university community. From a survey conducted at the beginning of the fall quarter, it was found that the University Bookstore and the Campus Bookstore each had 40% of the market, whereas the Book Mart had 20% of the market. Each quarter the University Bookstore retains 80% of its customers, but loses 5% to the Campus Bookstore and 15% to the Book Mart. The Campus Bookstore retains 90% of its customers, but loses 5% to the University Bookstore and 5% to the Book Mart. The Book Mart retains 70% of its customers, but loses 5% to the University Bookstore and 25% to the Campus Bookstore.
If these trends continue, what percent of the market will each store have at the beginning of the second quarter?  What percent of the market will each store have at the beginning of the third quarter?

Quizplus · Accepted Answer

The Answer of At a certain university, three bookstores - the University Bookstore, the Campus Bookstore, and the Book Mart - currently serve the university community. From a survey conducted at the beginning of the fall quarter, it was found that the University Bookstore and the Campus Bookstore each had 40% of the market, whereas the Book Mart had 20% of the market. Each quarter the University Bookstore retains 80% of its customers, but loses 5% to the Campus Bookstore and 15% to the Book Mart. The Campus Bookstore retains 90% of its customers, but loses 5% to the University Bookstore and 5% to the Book Mart. The Book Mart retains 70% of its customers, but loses 5% to the University Bookstore and 25% to the Campus Bookstore.
If these trends continue, what percent of the market will each store have at the beginning of the second quarter?  What percent of the market will each store have at the beginning of the third quarter?

At a Certain University, Three Bookstores - the University Bookstore