Set up systems of equations and solve by any appropriate method. All numbers are accurate to at least two significant digits.

An online merchandise company charges $4 for shipping orders of less than $50, $6 for orders from $50 to $200, and $8 for orders over $200. One day the total shipping charges were $2160 for 384 orders. Find the number of orders shipped at each rate if the number of orders under $50 was 12 more than twice the number of orders over $200.