SOLUTION: The son is 21 years younger than the mother. In six years she will be five times as old as him. What age will the son be?

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Question 847024: The son is 21 years younger than the mother. In six years she will be five times as old as him. What age will the son be?
Found 3 solutions by Alex Jordan, Fombitz, Alan3354:
Answer by Alex Jordan(2) About Me  (Show Source):
You can put this solution on YOUR website!
Here's my solution:
21+6+5=32.
Solution: So, the son will 32 years old.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Something is wrong with your problem setup.
S=M-21
In 6 years, she will be M+6 and the son will be S+6.
M%2B6=5%28S%2B6%29
Substitute eq. 1 into eq. 2,
M%2B6=5%28M-21%2B6%29
M%2B6=5%28M-15%29
M%2B6=5M-75
4M=81
M=81%2F4
Then the son would be,
S=81%2F4-21
S=81%2F4-84%2F4
S=-3%2F4
Typically the solutions are integers first off and secondly no negative ages are allowed.
I also changed the problem in case the mother is five times older than his age today.
M%2B6=5S
Then,
M%2B6=5%28M-21%29
M%2B6=5M-105
4M=111
M=111%2F4
and then
S=111%2F4-84%2F4
S=27%2F4
Again typically the solutions are in integers values.
Please check the problem and repost if needed.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The son is 21 years younger than the mother. In six years she will be five times as old as him. What age will the son be?
------------
s = m - 21 ******* Always 21 yrs difference
5(s + 6) = m + 6 ***** 6 yrs from now
--------
5s+30 = m+6
Sub for s
5(m-21) + 30 = m+6
5m - 75 = m + 6
4m = 81
m = 20.25
Makes the son's present age negative.
Not a good problem.