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.