To determine the maximum number of toppings that can be added to the large cheese pizza with $35 to spend, we can use the equation given for the cost function:
\[ c(n) = 16.5 + 2.5n \]
where \( c(n) \) is the total cost and \( n \) is the number of toppings.
Since the customer has $35 to spend, we set up the inequality:
\[ c(n) \leq 35 \]
Substituting the cost function into the inequality, we have:
\[ 16.5 + 2.5n \leq 35 \]
Now, we can solve for \( n \):
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Subtract 16.5 from both sides:
\[ 2.5n \leq 35 - 16.5 \]
\[ 2.5n \leq 18.5 \]
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Divide both sides by 2.5:
\[ n \leq \frac{18.5}{2.5} \]
\[ n \leq 7.4 \]
Since \( n \) must be a whole number (you can't add a fraction of a topping), we take the largest whole number less than or equal to 7.4.
Thus, the maximum number of toppings that can be added is:
\[ n = 7 \]
Therefore, the customer can add a maximum of 7 toppings to their large cheese pizza.