Builder Products, Incorporated, uses the weighted$-$average method of process costing It manufactures a caulking compound that goes through three processing stages prior to completion. Information on work in the first department, Cooking, is given below for May:

$\backslash$table$[[\backslash$table$[[$Pounds in process, May $1$ ; materials $100\%$ complete; conversion$],[90\%$ complete$]],85,000],[$Pounds started into production during May,$500,000],[$Pounds completed and transferred out,?$],[\backslash$table$[[$Pounds in process, May $31$ ; materials $80\%$ complete; conversion$],[20\%$ complete$]],45,000],[\backslash$table$[[$Cost data:$],[$Work in process inventory, May $1$:$]],],[$Materials cost$,$$$135,700$