Question 1014997
First off, you have an error.
You have $175 to start not $165.
{{{55+8p<=175}}}
{{{8p<=120}}}
{{{p<=15}}}
OK so at most you can have 15 people come. 
On the other end, you can have no one come ({{{p=0}}}).
So then this would be,
{{{0<=p<=15}}}
or in interval notation,
[0,15]