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Three market leaders in auto insurance in a state are State Farm, Progressive, and American Family Insurance. Based on data from a certain year, two relationships between the au Insurance percentage market shares are found to be as given below, where x, y, z, and w are the percentages of the market held by State Farm, Progressive, American Family, and other companies, respectively. x = y +4z-27 z = 15 - 2y+w Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, Progressive, and American Family depend on the share held by other companies. (Express your answer in terms of w, where x = x(w), y = y(w), and z = z(w).) (x, y, z) = Which of the three companies' market share is most affected by the share held by other companies? State Farm Progressive American Family Insurance Group

Three market leaders in auto insurance in a state are State Farm, Progressive, and American Family Insurance. Based on data from a certain year, two relationships between the au Insurance percentage market shares are found to be as given below, where x, y, z, and w are the percentages of the market held by State Farm, Progressive, American Family, and other companies, respectively. x = y +4z-27 z = 15 - 2y+w Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, Progressive, and American Family depend on the share held by other companies. (Express your answer in terms of w, where x = x(w), y = y(w), and z = z(w).) (x, y, z) = Which of the three companies' market share is most affected by the share held by other companies? State Farm Progressive American Family Insurance Group

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.CR: Chapter 1 Review
Problem 78CR
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Three market leaders in auto insurance in a state are State Farm, Progressive, and American Family Insurance. Based on data from a certain year, two relationships between the au insurance percentage market shares are found to be as given below, where x, y, z, and w are the percentages of the market held by State Farm, Progressive, American Family, and other companies, respectively. x y+4z 27 z 15-2y+w Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, Progressive, and American Family depend on the share held by other companies. (Express your answer in terms of w, where x = x(w), y = y(w), and z = z(w).) (x, y, z) = × ) x Which of the three companies' market share is most affected by the share held by other companies? State Farm Progressive American Family Insurance Group
Transcribed Image Text:Three market leaders in auto insurance in a state are State Farm, Progressive, and American Family Insurance. Based on data from a certain year, two relationships between the au insurance percentage market shares are found to be as given below, where x, y, z, and w are the percentages of the market held by State Farm, Progressive, American Family, and other companies, respectively. x y+4z 27 z 15-2y+w Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, Progressive, and American Family depend on the share held by other companies. (Express your answer in terms of w, where x = x(w), y = y(w), and z = z(w).) (x, y, z) = × ) x Which of the three companies' market share is most affected by the share held by other companies? State Farm Progressive American Family Insurance Group
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