Out of the 7920 visitors to an amusement park, 40% were children. Also, a fourth of the children and a third of the adults were repeat visitors. How many percent of the visitors were visiting the amusement park for the first time?
There were 7920 x 40/100 = <<7920*40/100=3168>>3168 children in the amusement park.
Out of these children, 3168 x 1/4 = <<3168*1/4=792>>792 were repeat visitors.
So, 3168 - 792 = <<3168-792=2376>>2376 children were visiting for the first time.
While there were 7920 - 3168 = <<7920-3168=4752>>4752 adults in the amusement park.
Out of these adults, 4752 x 1/3 = <<4752*1/3=1584>>1584 were repeat visitors.
So, 4752 - 1584 = <<4752-1584=3168>>3168 adults were visiting for the first time.
Hence, 2376 + 3168 = <<2376+3168=5544>>5544 visitors were visiting the amusement park for the first time.
Therefore, 5544/7920 x 100 = <<5544/7920*100=70>>70% of the visitors were visiting the amusement park for the first time. Answer: \boxed{70}.
To find the percentage of visitors who were visiting the amusement park for the first time, we need to subtract the percentage of repeat visitors from 100%.
First, let's find the number of children:
7920 visitors * 40% = 3168 children
Next, let's find the number of adults:
7920 visitors - 3168 children = 4752 adults
Now, let's find the number of repeat children:
3168 children * 1/4 = 792 repeat children
And the number of repeat adults:
4752 adults * 1/3 = 1584 repeat adults
Now, let's find the total number of repeat visitors:
792 repeat children + 1584 repeat adults = 2376 repeat visitors
Finally, let's find the percentage of visitors who were visiting for the first time:
100% - (2376 repeat visitors / 7920 total visitors) * 100% = 100% - 30% = 70%
Therefore, 70% of the visitors were visiting the amusement park for the first time.