A mail-order company charges $4 for shipping orders of less than $50, $6 for orders from $50- $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 is 12 more than twice the number of orders over $200.

I need three equations. I think one should be x+y+z=384 and another should be 4x+6y+8z=2160 but the third one really has me stuck. Any help is greatly appreciated. Thank you

Hint: the third equation comes from "the number of orders under $50 is 12 more than twice the number of orders over $200."