Question

The cost of a large cheese pizza at a local pizzeria can be modeled with the function C(n)=16.5+2.5n
, where n is the number of toppings that can be added on. If a customer has $35 to spend, what is the maximum number of toppings that they can add to their large cheese pizza?(1 point)
With $35 to spend, they can add a maximum of
toppings to the pizza.

Answer 1

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:

\[
\boxed{7}
\]