Percentage of a collection doubly grouped

Question

Suppose I have a collection of people.

I look at one specific group which contains 8% of total people.

I know in that group the average percentage of total sweets each person has is 3%.

I want to know what percentage of total sweets in the group.

Answer 1

Hopefully I have interpreted your question correctly (because it does not seem to make much sense):

• You say each person in the specific group has a proportion $0.03$ of total sweets.
• If there are $n$ people in that group then together they have $0.03n$ proportion of total sweets.
• If there are $m$ people in total then $n=0.08m$.
• But then the people in the group together have $0.03(0.08m)=0.0024m$ proportion of the total sweets.

The answer depends on $m$. Since it must be that $0.0024m\leq 1$, you need $m\leq 416$. (Also you require $m$ and $n$ are positive integers.)