Question: The Auburn–Washburn School District serves the Southern and Southwestern parts of a county with a population of what as of the 2010 census?

 As of the 2010 census, the population was 177,934 making it the third-most populous county in Kansas.  Its most populous city, Topeka, is the state capital and county seat.  The county was one of the original 33 counties created by the first territorial legislature in 1855, and it was named for the Shawnee tribe of Native Americans. Shawnee County (county code SN) is a county located in northeast Kansas, in the central United States of America. <SEP> The Belle Vernon Area School District is a midsized, suburban, public school district located approximately 25 mi southeast of Pittsburgh in rural Westmoreland County and Fayette County.  The present school district was formed by a merger of the previous Belmar (having itself been the result of a merge between the Belle Vernon and Marion school districts) and Rostraver school districts in 1965.  The district serves five political subdivisions located in 2 counties: Washington Township, Fayette City, North Belle Vernon, Belle Vernon, and Rostraver Township.  Belle Vernon Area School District area is 42.2 sqmi .  Belle Vernon Area School District in southwestern Pennsylvania lies midway between the cities of Pittsburgh on the north, Uniontown on the south, Washington to the west, and Greensburg to the east.  Belle Vernon Area School District had a population as of 2000 of 20,127 residents.  By 2010, the District's population declined to 18,912 people.  The educational attainment levels for the School District population (25 years old and over) were 91% high school graduates and 21.6% college graduates.  The District is one of the 500 public school districts of Pennsylvania. <SEP> Elk Lake School District is a small, rural, K-12 public school district with its only building located on State Route 3019 in Dimock, Susquehanna County, Pennsylvania.  It covers Auburn Township, Middletown Township, Rush Township, Dimock Township, and Springville Township in Susquehanna County, along with Meshoppen Borough and Meshoppen Township in Wyoming County.  The Elk Lake School District encompasses approximately 197 sqmi .  According to 2000 federal census data, Elk Lake School District serves a resident population of 7,735 people.  In 2009, the district residents’ per capita income was $15,355, while the median family income was $38,385.  In the Commonwealth, the median family income was $49,501 and the United States median family income was $49,445, in 2010.  In 2006, the district students are 97% white, less than 1% Asian, less than 1% black and 2% Hispanic.  According to District officials, in school year 2007-08 the Elk Lake School District provided basic educational services to 1,388 pupils through the employment of 114 teachers, 62 full-time and part-time support personnel, and 10 administrators. <SEP>  It serves Southern and Southwestern Shawnee County, as well as a small portion of extreme northern Osage County.  It serves Southwestern and Western portions of the City of Topeka, as well as the communities of Pauline, Montara, Auburn, and Wakarusa.  It has one primary school, one intermediate school, five elementary schools, one middle school, and one high school. The Auburn–Washburn School District (Kansas Unified School District #437) is a Unified school district in Topeka, Kansas.