A movie star, unwilling to give his age, posed the following riddle to a gossip columnist: "3 years ago, I was 9 times as old as my daughter. Now I am 6 times as old as she is." How old is the movie star?

Answer 1

Let's assume the current age of the movie star is 'M' and the current age of his daughter is 'D'.

According to the riddle, 3 years ago, the movie star was 9 times as old as his daughter. So, 3 years ago, the age of the movie star was (M - 3) and the age of his daughter was (D - 3). The equation for this statement can be written as:
(M - 3) = 9(D - 3)

Now, the riddle also states that currently, the movie star is 6 times as old as his daughter. So, the equation for this statement can be written as:
M = 6D

Now, we can solve these two equations simultaneously to find the values of M and D.

From the second equation, we can substitute M as 6D in the first equation:
(6D - 3) = 9(D - 3)

Expanding the equation:
6D - 3 = 9D - 27

Bringing similar terms together:
6D - 9D = -27 + 3
-3D = -24

Dividing both sides by -3:
D = -24 / -3
D = 8

Now that we know the daughter's age is 8, we can substitute this back into the second equation to find the movie star's age:
M = 6D
M = 6 * 8
M = 48

Therefore, the movie star is 48 years old.