Question 1163882: Two years ago a man was 7 times older than his son but in three years he will be only four times as old as his son.How old are they?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! m = number of years old the man is now.
s = number of years old his sone is now.
two years ago, the man was 7 times older than his son.
there is a difference between 7 times as old and 7 times older.
7 times as old says that a = 7 * b
7 times older says that a = b + 7*b = 8*b
your problem statement seems to mix them both.
i suspect you meant as old as, rather than older than.
i'll assume that, therefore, i'll rephrase the problem statement to say:
Two years ago a man was 7 times as old as his son, but in three years he will be only four times as old as his son.
How old are they?
your formulas are:
(m - 2) = 7 * (s - 2)
(m + 3) = 4 * (s + 3)
simplify these formulas to get:
m - 2 = 7 * s - 14
m + 3 = 4 * s + 12
solve for m in both equations to get:
m = 7 * s - 12
m = 4 * s + 9
subtract the second equation from the first to get 0 = 3 * s - 21
add 21 to both sides of this equation to get 21 = 3 * s
solve for s to get s = 7
2 years ago, the son was 5 and the man was 7 * 5 = 35
that means the man is currently 37 years old and his son is 7.
3 years from now, the man will be 40 and his son will be 10.
40 / 10 = 4 which means that the man will be 4 times as old as his son.
looks like man is 37 years old and his son is 7.
two years ago, 35/5 = 7
3 years from now, 40/10 = 4
solution looks good.
solution is man is 37 years old and his son is 7.
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