Question 751452: Currently Doris is one year older than twice Arthurs age. In ten years time the sum of their ages will be 39. Determine their current ages now.
Answer by kmadison(20)   (Show Source):
You can put this solution on YOUR website! Pick all numbers that sum to 39: (39+0),(38+1),(37+2),(36+3),(35+4),(34+5),(33+6),(32+7),(31+8),(30+9),(29+10),(28+11),(27+12),(26+13),(25+14), (24+15),(23+16),(22+17),(21+18),(20+19). We can stop here because all other pairs will repeat.
Now remembering that we are subtracting 10 from each, we can reasonably eliminate anything 29+ since a negative number is unreasonable for an age, and an age of 0 would indicate 1 of them has not yet been born. This leaves (28+11),(27+12),(26+13),(25+14), (24+15),(23+16),(22+17),(21+18),(20+19) as possible contenders.
This is where we look at the 1st condition: Doris is currently 2x+1 years older than Arthur. Subtracting 10 from each pair gives us respectively: (18,1);(17,2);(16,3);(15,4);(14,5);(13,6);(12,7);(11,8);(10,9). From here we plug each pair into our equation 2x+1 and find only 1 pair satisfies the equation: (13,6) 
So the final answer is: Doris is currently 13, Arthur is currently 6.
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