Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of x one-bedroom units, y two-bedroom townhouses, and z three-bedroom townhouses. A total of 186 units are planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex.

Answer:The x one bedroom is 93 unit, y two-bedroom is 62 units, and z three-bedroom is 31 units.Step-by-step explanation:Consider the provided information.A total of 186 units are planned,Apartment complex consisting of x one-bedroom units, y two-bedroom townhouses, and z three-bedroom townhouses. This can be written as:[tex]x + y + z = 186[/tex]   ......(1)The number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units.[tex]x = y+z[/tex]   ......(2)The number of one-bedroom units will be 3 times the number of three-bedroom units,[tex]x = 3z[/tex]    ......(3)From 3 and 2.[tex]3z-z=y[/tex] [tex]2z=y[/tex] Substitute the value of x and y in equation 1.[tex]3z+ 2z + z = 186[/tex][tex]6z= 186[/tex][tex]z= 31[/tex]Substitute the value of z in equation 3[tex]x = 3(31)[/tex][tex]x =93[/tex]Substitute the value of z in [tex]2z=y[/tex] [tex]2(31)=y[/tex]  [tex]62=y[/tex]  Thus, the x one bedroom is 93 unit, y two-bedroom is 62 units, and z three-bedroom is 31 units.