June's father is 6 times as old as June. The sum of their ages is no less than 77.

X represents June's age:

6x (father) + x (June) = 77

6x+x=77

7x=77

x=77:7

x=11

June is 11 years old.

Her father is 6 times as old.

So, 11*6=66. June's father is 66 years old.

Now check:

11+66=77 (sum together)

and 66:11=6 (6 times older)