Given:
Total budget = $3500
The hall charges a $50 clean up fee plus $38 per person
Let the number of persons = x
So, the total cost = 38x + 50
The greatest number of people will follow the inequality:
[tex]38x+50\le3500[/tex]solve for x:
[tex]\begin{gathered} 38x\le3500-50 \\ 38x\le3450 \\ x\le\frac{3450}{38} \\ \\ x\le90.789 \end{gathered}[/tex]So, the answer will be:
The greatest number of people they can invite = 90 persons
