The sum of Grover's age and that of his friend Harold is 180 years. Thirty years ago, Grover was 3 times as old as Harold was then. How old are Grover and Harold?

Let Grover's age now be g.

Let Harold's age now be h.

Now:

The sum of Grover’s age and that of his friend Harold is 180 years.

g + h = 180 Equation 1

30 years ago, Grover's age was g - 30, and Harold's age was h - 30.

Thirty years ago, Grover was 3 times as old as Harold was then.

g - 30 = 3 (h - 30) Equation 2

We have two unknowns, g and h, and two unknowns, g and h.

We can solve the system of equations for g and h.

g + h = 180

g - 30 = 3 (h - 30)

Simplify the second equation and solve for g.

g - 30 = 3h - 90

g = 3h - 60

Now substitute 3h - 60 in for g in the first equation.

g + h = 180

3h - 60 + h = 180

4h - 60 = 180

4h = 240

h = 60

Now we use the first equation to find g.

g + h = 180

g + 60 = 180

g = 120

Answer: Grover is 120 years old, and Harold is 60 years old.