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

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

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