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 $w,$wherex$=x(w),y=y(w),$ 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