Book Maths Puzzle Age Problem

In an organization there are CE's, ME's and EE's. The sum of their ages is 2160; the average age is 36; the average age of the CE's and ME's is 39; the average age of the ME's and EE's is 32 8/11; the average age of the CE's and EE's is 36 2/3. If each CE had been 1 year older, each ME 6 years and each EE 7 years older, their average age would have been greater by 5 years. Find the number of each group and their average ages.

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