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?
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.
Let's solve this step-by-step:
Let's assume the current age of the movie star is "X" years old.
Let's assume the current age of the movie star's daughter is "Y" years old.
According to the information given, 3 years ago, the movie star's age was 9 times the age of his daughter. So, we can write the equation as:
(X - 3) = 9(Y - 3)
Now, the movie star's current age is 6 times the age of his daughter. So, we can write the equation as:
X = 6Y
We have two equations:
(X - 3) = 9(Y - 3)
X = 6Y
We can solve this system of equations by substituting the value of X from the second equation into the first equation:
6Y - 3 = 9(Y - 3)
6Y - 3 = 9Y - 27
27 - 3 = 9Y - 6Y
24 = 3Y
Y = 8
Now, substitute the value of Y back into the second equation to find the value of X:
X = 6Y
X = 6(8)
X = 48
Therefore, the movie star is 48 years old.