Metros that Cross State Lines

Greetings,
I am wrangling with a problem related to metros that cross state lines (specifically the list below). Is there a way to determine the count/percent of people that live in each state?

For example, the population of Providence-Warwick is 1,675,774. Providence has a pop of 189,575 and Warwick has a pop of 83,024. That's only equal to 272,599. Where does the remainder live? 

Columbus GA-AL
Davenport-Moline-Rock Island IA-IL
Lewiston ID-WA
Cumberland MD-WV
Hagerstown-Martinsburg MD-WV
Salisbury MD-DE
Minneapolis-St. Paul-Bloomington MN-WI
Cincinnati OH-KY-IN
Providence-Warwick RI-MA
Myrtle Beach-Conway-North Myrtle Beach SC-NC
Chattanooga TN-GA
Clarksville TN-KY
Kingsport-Bristol TN-VA
Memphis TN-MS-AR
Texarkana TX-AR

Thanks!
Derek