Question
Noah discovered that a 17-in.-diameter pizza costs $19.00. A 12-in.-diameter pizza costs $14.00. The 12-in.-diameter pizza is cut into six slices. The 17-in.-diameter pizza is cut into eight slices. Use 3.14 for pi.
Question content area bottom
Part 1
(a) What is the cost per slice of the 17-in.-diameter pizza?
$
enter your response here (Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 2
How many square inches of pizza are in one slice?
enter your response here in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 3
(b) What is the cost per slice of the 12-in.-diameter pizza?
$
enter your response here (Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 4
How many square inches of pizza are in one slice?
enter your response here in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 5
(c) If you want more value for your money, which slice of pizza should you buy?
17-in.-diameter pizza
12-in.-diameter pizza
Question content area bottom
Part 1
(a) What is the cost per slice of the 17-in.-diameter pizza?
$
enter your response here (Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 2
How many square inches of pizza are in one slice?
enter your response here in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 3
(b) What is the cost per slice of the 12-in.-diameter pizza?
$
enter your response here (Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 4
How many square inches of pizza are in one slice?
enter your response here in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 5
(c) If you want more value for your money, which slice of pizza should you buy?
17-in.-diameter pizza
12-in.-diameter pizza
Answers
GPT-4o mini
To solve the problem step by step, we will first calculate the area of each pizza, determine the area per slice for both sizes, and then calculate the cost per slice for each pizza.
### Part 1: 17-in-Diameter Pizza
1. **Calculate the area of the pizza.**
\[
\text{Area} = \pi r^2
\]
The radius \( r \) is half of the diameter, so for a 17-inch pizza:
\[
r = \frac{17}{2} = 8.5 \text{ in}
\]
Now calculate the area:
\[
\text{Area} = 3.14 \times (8.5)^2 = 3.14 \times 72.25 \approx 226.85 \text{ in}^2
\]
2. **Calculate the cost per slice.**
The pizza is cut into 8 slices.
\[
\text{Cost per slice} = \frac{\text{Total cost}}{\text{Number of slices}} = \frac{19.00}{8} \approx 2.375
\]
When rounded to the nearest hundredth:
\[
\text{Cost per slice} \approx 2.38
\]
### Part 2: Area per slice for the 17-in-Diameter Pizza
1. **Calculate the area per slice.**
\[
\text{Area per slice} = \frac{\text{Total area}}{\text{Number of slices}} = \frac{226.85}{8} \approx 28.35625
\]
When rounded to the nearest hundredth:
\[
\text{Area per slice} \approx 28.36 \text{ in}^2
\]
### Part 3: 12-in-Diameter Pizza
1. **Calculate the area of the pizza.**
The radius \( r \) for a 12-inch pizza:
\[
r = \frac{12}{2} = 6 \text{ in}
\]
Now calculate the area:
\[
\text{Area} = 3.14 \times (6)^2 = 3.14 \times 36 \approx 113.04 \text{ in}^2
\]
2. **Calculate the cost per slice.**
The pizza is cut into 6 slices.
\[
\text{Cost per slice} = \frac{14.00}{6} \approx 2.3333
\]
When rounded to the nearest hundredth:
\[
\text{Cost per slice} \approx 2.33
\]
### Part 4: Area per slice for the 12-in-Diameter Pizza
1. **Calculate the area per slice.**
\[
\text{Area per slice} = \frac{\text{Total area}}{\text{Number of slices}} = \frac{113.04}{6} \approx 18.84
\]
When rounded to the nearest hundredth:
\[
\text{Area per slice} \approx 18.84 \text{ in}^2
\]
### Part 5: Value for Money
Now to determine which slice of pizza gives more value for your money, we can look at the area per dollar spent for both pizzas.
**For the 17-in pizza:**
\[
\text{Area per dollar} = \frac{\text{Area per slice}}{\text{Cost per slice}} = \frac{28.36}{2.38} \approx 11.91 \text{ in}^2/\$
\]
**For the 12-in pizza:**
\[
\text{Area per dollar} = \frac{\text{Area per slice}}{\text{Cost per slice}} = \frac{18.84}{2.33} \approx 8.09 \text{ in}^2/\$
\]
### Conclusion
Since \( 11.91 \text{ in}^2/\$ > 8.09 \text{ in}^2/\$ \), you should buy the **17-in-diameter pizza** for better value for your money.
### Summary of Answers:
- Part 1: Cost per slice of the 17-in pizza: **$2.38**
- Part 2: Area per slice of the 17-in pizza: **28.36 in²**
- Part 3: Cost per slice of the 12-in pizza: **$2.33**
- Part 4: Area per slice of the 12-in pizza: **18.84 in²**
- Part 5: Buy the **17-in-diameter pizza**.
### Part 1: 17-in-Diameter Pizza
1. **Calculate the area of the pizza.**
\[
\text{Area} = \pi r^2
\]
The radius \( r \) is half of the diameter, so for a 17-inch pizza:
\[
r = \frac{17}{2} = 8.5 \text{ in}
\]
Now calculate the area:
\[
\text{Area} = 3.14 \times (8.5)^2 = 3.14 \times 72.25 \approx 226.85 \text{ in}^2
\]
2. **Calculate the cost per slice.**
The pizza is cut into 8 slices.
\[
\text{Cost per slice} = \frac{\text{Total cost}}{\text{Number of slices}} = \frac{19.00}{8} \approx 2.375
\]
When rounded to the nearest hundredth:
\[
\text{Cost per slice} \approx 2.38
\]
### Part 2: Area per slice for the 17-in-Diameter Pizza
1. **Calculate the area per slice.**
\[
\text{Area per slice} = \frac{\text{Total area}}{\text{Number of slices}} = \frac{226.85}{8} \approx 28.35625
\]
When rounded to the nearest hundredth:
\[
\text{Area per slice} \approx 28.36 \text{ in}^2
\]
### Part 3: 12-in-Diameter Pizza
1. **Calculate the area of the pizza.**
The radius \( r \) for a 12-inch pizza:
\[
r = \frac{12}{2} = 6 \text{ in}
\]
Now calculate the area:
\[
\text{Area} = 3.14 \times (6)^2 = 3.14 \times 36 \approx 113.04 \text{ in}^2
\]
2. **Calculate the cost per slice.**
The pizza is cut into 6 slices.
\[
\text{Cost per slice} = \frac{14.00}{6} \approx 2.3333
\]
When rounded to the nearest hundredth:
\[
\text{Cost per slice} \approx 2.33
\]
### Part 4: Area per slice for the 12-in-Diameter Pizza
1. **Calculate the area per slice.**
\[
\text{Area per slice} = \frac{\text{Total area}}{\text{Number of slices}} = \frac{113.04}{6} \approx 18.84
\]
When rounded to the nearest hundredth:
\[
\text{Area per slice} \approx 18.84 \text{ in}^2
\]
### Part 5: Value for Money
Now to determine which slice of pizza gives more value for your money, we can look at the area per dollar spent for both pizzas.
**For the 17-in pizza:**
\[
\text{Area per dollar} = \frac{\text{Area per slice}}{\text{Cost per slice}} = \frac{28.36}{2.38} \approx 11.91 \text{ in}^2/\$
\]
**For the 12-in pizza:**
\[
\text{Area per dollar} = \frac{\text{Area per slice}}{\text{Cost per slice}} = \frac{18.84}{2.33} \approx 8.09 \text{ in}^2/\$
\]
### Conclusion
Since \( 11.91 \text{ in}^2/\$ > 8.09 \text{ in}^2/\$ \), you should buy the **17-in-diameter pizza** for better value for your money.
### Summary of Answers:
- Part 1: Cost per slice of the 17-in pizza: **$2.38**
- Part 2: Area per slice of the 17-in pizza: **28.36 in²**
- Part 3: Cost per slice of the 12-in pizza: **$2.33**
- Part 4: Area per slice of the 12-in pizza: **18.84 in²**
- Part 5: Buy the **17-in-diameter pizza**.