Let us prepare an inequality statement to answer the question.
There is a one-time fee of $85 and a fee of $23 per guest. If x represents the number of guests, the amount spent will be:
[tex]85+23x[/tex]
If the amount spent cannot exceed $1750, we have the inequality statement to be:
[tex]85+23x\leq1750[/tex]
We can solve as follows:
[tex]\begin{gathered} 23x\leq1750-85 \\ 23x\leq1665 \\ x\leq\frac{1665}{23} \\ x\leq72.39 \end{gathered}[/tex]
Since we cannot have a fraction of a person, the answer will be 72.
her maximum number of guests is 72.
