SOLUTION: (c) A is eleven times as old as B. In a certain number of years A will be five times as old as B, and five year after that A will be three times as old as B. How old are they now?

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Question 679031: (c) A is eleven times as old as B. In a certain number of years A will be five times as old as B, and five year after that A will be three times as old as B. How old are they now?
Answer by pmatei(79) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+11B
A+%2B+n+=+5%28B%2Bn%29
A+%2B+n+%2B+5+=+3%28B+%2B+n+%2B+5%29
In the last 2 equations replace A with 11B (first equation) and distribute on the right side of the equations:
11B+%2B+n+=+5B+%2B+5n
11B+%2B+n+%2B+5+=+3B+%2B+3n+%2B15
Bring the right side B-terms in the left side and the n's and 5 from the left side to the right side:
6B+=+4n
8B+=+2n+%2B+10
Divide by 2 the first equation:
3B+=+2n
8B+=+2n+%2B+10
Subtract first equation from the second one:
5B+=+10
B+=+2
A+=+11B+=+22
In n=3 years A=25 and B=5 (A five times older than B), and five years after that A+=+30 and B=10 (A three times older than B).