Weird Doctors' Stalker
In an organization, there are engineers, accountants and doctors. The sum of the ages is 2,160; the average age is 36. The average age of the engineers and accountants is 39; of the accountants and doctors, 32 & 8/11; the engineers and doctors, 36 & 2/3. If each engineer were 1 year older, each accountant 6 years older, and each doctor 7 years older, their average age would be 41. Determine the number of doctors.
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1 solution
It's easy but had a very long solution!
10.Combine #2 and #4--> 39(nE+nA)+D=2,160
11.Combine #2 and #5--> (360/11)(nA+nD)+E=2,160 12.Combine #2 and #6--> (110/3)(nE+nD)+A=2,160
13.Add #10,#11 and #12 to have: [(227nE)/3]+[(789nA)/11]+[(2,290nD)/33]=4320
14.Solving numbers(#) 8, 9, and 13 we obtain nE=16, nA=24, and nD=20. So the answer is 20!