Three market leaders in homeowners insurance in a state are State Farm, American Family Insurance Group, and Allstate. Based on data from a certain year, two relationships between the homeowners 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, American Family, Allstate, and other companies, respectively. x = −42 + 5y + z z = 5 − 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, American Family, and Allstate 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 FarmAmerican Family Insurance Group Allstate

Three market leaders in homeowners insurance in a state are State Farm, American Family Insurance Group, and Allstate. Based on data from a certain year, two relationships between the homeowners 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, American Family, Allstate, and other companies, respectively. x = −42 + 5y + z z = 5 − 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, American Family, and Allstate 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 FarmAmerican Family Insurance Group Allstate

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Three market leaders in homeowners insurance in a state are State Farm, American Family Insurance Group, and Allstate. Based on data from a certain year, two relationships between the homeowners 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, American Family, Allstate, and other companies, respectively. x = −54 + 5y + z z = 9 − 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, American Family, and Allstate 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?
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