To determine the maximum number of toppings a customer can add to a large cheese pizza given their budget of $35, we can set up the following equation based on the cost function:
\[ C(n) = 16.5 + 2.5n \]
We want to find the maximum number of toppings \(n\) such that:
\[ C(n) \leq 35 \]
Substituting the cost function into the inequality gives:
\[ 16.5 + 2.5n \leq 35 \]
Now, subtract 16.5 from both sides:
\[ 2.5n \leq 35 - 16.5 \]
This simplifies to:
\[ 2.5n \leq 18.5 \]
Next, divide both sides by 2.5:
\[ n \leq \frac{18.5}{2.5} \]
Calculating the right-hand side:
\[ \frac{18.5}{2.5} = 7.4 \]
Since \(n\) must be a whole number (you can't add a fraction of a topping), we round down to the nearest whole number:
\[ n \leq 7 \]
Thus, the maximum number of toppings that can be added to the pizza is:
\[ \boxed{7} \]