3. You currently drive 240 miles per week in a car that gets 16 miles per gallon. A new car cost $13,000 (after trade-in) and gets 40 miles per gallon. Insurance and repairs for the old car are $600 per year and $1400 per year, respectively. The insurance for the new car is $800 per year and there are no repair costs for the first 5 years. Assume gas costs $3.50 per gallon for the next 5 years. (a) What is the cost of keeping your old car for the next 5 years? (b) What is the cost of the new car for the next 5 years? (c) How much money might you save by choosing the less expensive option?
3. You currently drive 240 miles per week in a car that gets 16 miles per gallon. A new car cost $13,000 (after trade-in) and gets 40 miles per gallon. Insurance and repairs for the old car are $600 per year and $1400 per year, respectively. The insurance for the new car is $800 per year and there are no repair costs for the first 5 years. Assume gas costs $3.50 per gallon for the next 5 years. (a) What is the cost of keeping your old car for the next 5 years? (b) What is the cost of the new car for the next 5 years? (c) How much money might you save by choosing the less expensive option?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Currently drive 240 miles per week in a car they get 16 miles per gallon. A new car cost $13,000…. (See photo)
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### Cost Analysis of Keeping an Old Car vs. Buying a New Car
#### Problem Statement:
You currently drive 240 miles per week in a car that gets 16 miles per gallon. A new car costs $13,000 (after trade-in) and gets 40 miles per gallon. Insurance and repairs for the old car are $600 per year and $1400 per year, respectively. The insurance for the new car is $800 per year and there are no repair costs for the first 5 years. Assume gas costs $3.50 per gallon for the next 5 years.
**(a) What is the cost of keeping your old car for the next 5 years?**
**(b) What is the cost of the new car for the next 5 years?**
**(c) How much money might you save by choosing the less expensive option?**
#### Solution:
**(a) Cost of Keeping the Old Car for the Next 5 Years**
1. **Fuel Costs**:
- Weekly miles driven = 240 miles
- Miles per gallon for old car = 16 MPG
- Cost per gallon of gas = $3.50
\[
\text{Fuel consumed per week} = \frac{240 \text{ miles}}{16 \text{ MPG}} = 15 \text{ gallons/week}
\]
\[
\text{Cost of fuel per week} = 15 \text{ gallons/week} \times \$3.50/\text{gallon} = \$52.50/\text{week}
\]
\[
\text{Annual fuel cost} = \$52.50/\text{week} \times 52 \text{ weeks/year} = \$2730/year
\]
\[
\text{Cost over 5 years} = \$2730/year \times 5 \text{ years} = \$13650
\]
2. **Insurance Costs**:
\[
\text{Yearly insurance cost} = \$600/year
\]
\[
\text{5-year insurance cost} = \$600/year \times 5 \text{ years} = \$3000
\]
3. **Repair Costs**:
\[
\text{Yearly repair cost} = \$1400/year
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2527d55-bafb-4364-9044-dce9e5596181%2F90ac5fd2-1040-453c-8cdb-3ac72972451a%2Ffthlnk9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Cost Analysis of Keeping an Old Car vs. Buying a New Car
#### Problem Statement:
You currently drive 240 miles per week in a car that gets 16 miles per gallon. A new car costs $13,000 (after trade-in) and gets 40 miles per gallon. Insurance and repairs for the old car are $600 per year and $1400 per year, respectively. The insurance for the new car is $800 per year and there are no repair costs for the first 5 years. Assume gas costs $3.50 per gallon for the next 5 years.
**(a) What is the cost of keeping your old car for the next 5 years?**
**(b) What is the cost of the new car for the next 5 years?**
**(c) How much money might you save by choosing the less expensive option?**
#### Solution:
**(a) Cost of Keeping the Old Car for the Next 5 Years**
1. **Fuel Costs**:
- Weekly miles driven = 240 miles
- Miles per gallon for old car = 16 MPG
- Cost per gallon of gas = $3.50
\[
\text{Fuel consumed per week} = \frac{240 \text{ miles}}{16 \text{ MPG}} = 15 \text{ gallons/week}
\]
\[
\text{Cost of fuel per week} = 15 \text{ gallons/week} \times \$3.50/\text{gallon} = \$52.50/\text{week}
\]
\[
\text{Annual fuel cost} = \$52.50/\text{week} \times 52 \text{ weeks/year} = \$2730/year
\]
\[
\text{Cost over 5 years} = \$2730/year \times 5 \text{ years} = \$13650
\]
2. **Insurance Costs**:
\[
\text{Yearly insurance cost} = \$600/year
\]
\[
\text{5-year insurance cost} = \$600/year \times 5 \text{ years} = \$3000
\]
3. **Repair Costs**:
\[
\text{Yearly repair cost} = \$1400/year
\]
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