Let a, b, c, d, e, f, g, h, i represent the nine people receiving jelly beans

Let's also say that, when we arrange the values in ascending order we get: a ≤ b ≤ c ≤ d ≤ e ≤ f ≤ g ≤ h ≤ i

Our goal is to MAXIMIZE the value of i/a

To do this, we must MAXIMIZE the value of i and MINIMIZE the value of a

GIVEN: no one receives fewer than 5 jellybeans
So, 5 is the MINIMUM value of a
We get: 5 ≤ b ≤ c ≤ d ≤ e ≤ f ≤ g ≤ h ≤ i

The 3 people with the most jellybeans have 60 jellybeans among them
We can write: g + h + i = 60
This also means that the 6 people with fewer jelly beans must have 40 jellybeans among them.
We can write: 5 + b + c + d + e = 40

IMPORTANT: We need values of b, c, d, e, and f that both satisfy the above equation AND minimize the value of f.
We need to minimize the value of f, so that we can minimize the values of g, h and i
The best we can do is as follows: 5 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ g ≤ h ≤ i

When we minimize the values of g and h, we get: 5 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ i

Finally, since the sum of all 9 numbers is 100, i must equal 46

We get: 5 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ 7 ≤ 46

So the maximum value of i/a = 46/5

Answer: 46/5

Cheers,
Brent