Number of Civil, Electrical, and Mechanical Engineers and Their Average Ages

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

Solution

 

In, "If each CE had been 1 year older, each EE 6 years and each ME 7 years older, their average age would have been greater by 5 years", why is it that you added 1 to c, 6 to e, and 7 to m wherein c, e, and m are the average ages of CE, EE, and ME, respectively? Will that make your provided equation wrong because the statement said if "each" engineer had been 1 year older and so on..?