Age Problem: Dr. Johnson and His Son

Problem Statement

Dr. Johnson is currently four times the age of his son. In twenty years, he will be twice as old as his son. The question is: How old are they now?

Solution

To find their current ages, let’s define the variables:
– Let y represent Dr. Johnson’s age.
– Let x represent his son’s age.

From the information provided, we can set up the following equations:
1. y = 4x (Dr. Johnson is four times as old as his son)
2. y + 20 = 2(x + 20) (In twenty years, he will be twice as old)

Now, we can solve this system of equations.

By substituting the first equation into the second:
4x + 20 = 2(x + 20)

Expanding and simplifying:
4x + 20 = 2x + 40
2x = 20
x = 10

Now that we have the son’s age, we can find Dr. Johnson’s age:
y = 4x
y = 4(10) = 40

Conclusion

Dr. Johnson is currently 40 years old, while his son is 10 years old.