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.
With $35 to spend, they can add a maximum of ? toppings to the pizza.
Answers
GPT-4o mini
To find the maximum number of toppings that can be added to a large cheese pizza with a budget of $35, we start with the cost function:
\[ C(n) = 16.5 + 2.5n \]
where \( n \) is the number of toppings. We want to set the cost equal to the budget:
\[ C(n) \leq 35 \]
\[ 16.5 + 2.5n \leq 35 \]
Next, we can solve for \( n \):
1. Subtract 16.5 from both sides:
\[ 2.5n \leq 35 - 16.5 \]
\[ 2.5n \leq 18.5 \]
2. 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 have a fraction of a topping), we round down to the nearest whole number:
\[ n \leq 7 \]
Therefore, the maximum number of toppings that can be added to the pizza is **7**.
\[ C(n) = 16.5 + 2.5n \]
where \( n \) is the number of toppings. We want to set the cost equal to the budget:
\[ C(n) \leq 35 \]
\[ 16.5 + 2.5n \leq 35 \]
Next, we can solve for \( n \):
1. Subtract 16.5 from both sides:
\[ 2.5n \leq 35 - 16.5 \]
\[ 2.5n \leq 18.5 \]
2. 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 have a fraction of a topping), we round down to the nearest whole number:
\[ n \leq 7 \]
Therefore, the maximum number of toppings that can be added to the pizza is **7**.