A certain man is 3 times as old as his son was when he was as old as
his son is now. What percent of the man's age is the son's age now?
Let M = the man's age now
Let S = the son's age now
Let x = the number of years it has been since the father was the son'd
present age.
M - x = the man's age x years ago
S - x = the son's age x years ago
= 3×
M = 3(S - x)
= 
M - x = S
So we have this system of equations:
M = 3(S - x)
M - x = S
Solve the second equation for x
x = M - S
Substitute in the first equation
M = 3(S - x)
M = 3[S - (M - S)]
M = 3[S - M + S]
M = 3[2S - M]
M = 6S - 3M
4M = 6S
EDivide both sides by 6
M = S
M = S
Therefore the son is or 
% of the man's age.
Here are the feasible possibilities:
The man is 63 years old and the son is 42 years old.
21 years ago, the man was 42 and the son was 21,
so the man's age now, which is 63, is 3 times the son's age
then, which was 21.
The man is 66 years old and the son is 44 years old.
22 years ago, the man was 44 and the son was 22,
so the man's age now, which is 66, is 3 times the son's age
then, which was 22.
The man is 69 years old and the son is 46 years old.
23 years ago, the man was 46 and the son was 23,
so the man's age now, which is 69, is 3 times the son's age
then, which was 23.
The man is 72 years old and the son is 48 years old.
24 years ago, the man was 48 and the son was 24,
so the man's age now, which is 72, is 3 times the son's age
then, which was 24.
The man is 75 years old and the son is 50 years old.
25 years ago, the man was 50 and the son was 25,
so the man's age now, which is 75, is 3 times the son's age
then, which was 25.
The man is 78 years old and the son is 52 years old.
26 years ago, the man was 52 and the son was 26,
so the man's age now, which is 78, is 3 times the son's age
then, which was 26.
The man is 81 years old and the son is 54 years old.
27 years ago, the man was 54 and the son was 27,
so the man's age now, which is 81, is 3 times the son's age
then, which was 27.
The man is 84 years old and the son is 56 years old.
28 years ago, the man was 56 and the son was 28,
so the man's age now, which is 84, is 3 times the son's age
then, which was 28.
The man is 87 years old and the son is 58 years old.
29 years ago, the man was 58 and the son was 29,
so the man's age now, which is 87, is 3 times the son's age
then, which was 29.
The man is 90 years old and the son is 60 years old.
30 years ago, the man was 60 and the son was 30,
so the man's age now, which is 90, is 3 times the son's age
then, which was 30.
The man is 93 years old and the son is 62 years old.
31 years ago, the man was 62 and the son was 31,
so the man's age now, which is 93, is 3 times the son's age
then, which was 31.
The man is 96 years old and the son is 64 years old.
32 years ago, the man was 64 and the son was 32,
so the man's age now, which is 96, is 3 times the son's age
then, which was 32.
The man is 99 years old and the son is 66 years old.
33 years ago, the man was 66 and the son was 33,
so the man's age now, which is 99, is 3 times the son's age
then, which was 33.
Edwin
