How do you find the total amount of a group when the given are percentages and an absolute count of a portion of the group?

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Let's say you an unknown number of members of a group, and they split up to go to the following locations:

Park: 35% of the members

School: 20% of the members

Post office: 15% of the members

Library: 10% of the members

Community Center: 4 members

Given four percentages (Park, School, Post Office, Library) and one absolute count (Community Center) - how many total members are there?

Here's what I've tried

The total of the four percentages equals: 80%. Therefore, that suggests that the 4 members who went to the Community Center equates to: 20% since that then completely totals 100%. $$ \verb|M = total members| $$ So, the Community Center equals:

$$ \verb|20% of M = 0.20M| $$

There are 4 members at the Community Center:

$$ 0.20M = 4 $$

$$ M = \frac{4}{0.20} $$

$$ M = 20 $$

However, I am just unsure if this is the correct answer let alone if I'm solving this type of problem correctly. Can someone give me some guidance on how to solve this problem and whether or not I am correct?