SOLUTION: Cary is 6 years older than Dan. In 9 years the sum of their ages will be 100. Find the age of each man now.

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Question 1149318: Cary is 6 years older than Dan. In 9 years the sum of their ages will be 100. Find the age of each man now.
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let Dan's age = +x+
Cary's age is +x+%2B+6+
-----------------------------
+%28+x+%2B+9+%29+%2B+%28+x+%2B+6+%2B+9+%29+=+100+
+2x+%2B+24+=+100+
+2x+=+76+
+x+=+38+
and
+x+%2B+6+=+44+
--------------------
Dan is 38
Cary is 44

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
You can easily solve it MENTALLY in your head, without using equation/equations. 

(1)  In 9 years the sum of their ages will be 100 ---- hence, now the sum of their ages is  100-2*9 = 100-18 = 82.



(2)  Cary is 6 years older than Dan and the sum of their ages is 82.



     Take half of 82, which is 41, and SUBTRACT half of 6, i.e. 3, from 41 --- you will get  41-3 = 38 years.

     It is the age of the younger men, Dan.



     Take half of 82 again, which is 41, and ADD half of 6, i.e. 3, to it --- you will get  41+3 = 44 years.

     It is the age of the older men, Cary.

Solved.