Rolando drives at least 40 miles but less than 60 miles each week. A. Graph the compound inequality representing all of the possible distances Rolando could drive for 8 weeks. You may copy and paste the number line image into a document, use it to answer the question, save, then attach the image to this question. Rolando's Driving for 8 Weeks + +11 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 Miles Driven B. Explain why you chose to use the symbols you used for the endpoints of the compound inequality in part A. C. Rolando buys at least 8.5 but no more than 11 gallons of gas each week. The price of gas has ranged from $2.40 to $2.65 per gallon each week. Write an inequality to model all of the possible amounts of money (m) Rolando spends on gas each week. Show or explain all your work.
Rolando drives at least 40 miles but less than 60 miles each week. A. Graph the compound inequality representing all of the possible distances Rolando could drive for 8 weeks. You may copy and paste the number line image into a document, use it to answer the question, save, then attach the image to this question. Rolando's Driving for 8 Weeks + +11 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 Miles Driven B. Explain why you chose to use the symbols you used for the endpoints of the compound inequality in part A. C. Rolando buys at least 8.5 but no more than 11 gallons of gas each week. The price of gas has ranged from $2.40 to $2.65 per gallon each week. Write an inequality to model all of the possible amounts of money (m) Rolando spends on gas each week. Show or explain all your work.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Rolando's Driving and Gas Usage: Exploring Compound Inequalities**
Rolando drives at least 40 miles but less than 60 miles each week. Let's explore the ways we can represent and interpret this information using inequalities and analyze his potential spending on gas.
**A. Graphing the Compound Inequality**
To represent all possible distances Rolando could drive over 8 weeks, use the compound inequality for weekly driving:
- Minimum distance: 40 miles/week
- Maximum distance: less than 60 miles/week
For 8 weeks, the total distance range is:
\[ 40 \times 8 \leq x < 60 \times 8 \]
\[ 320 \leq x < 480 \]
On the number line, the graph is a segment starting from 320 and ending before 480, indicating that the total distance driven ranges from 320 to just under 480 miles.
**Graph Explanation:**
The number line marks increments of 40 miles, from 40 to 600 miles. The range of interest where Rolando might drive is highlighted from 320 to just under 480 miles, representing possible total driving distances for 8 weeks.
**B. Explanation of Symbols for Endpoints**
In the compound inequality \( 320 \leq x < 480 \):
- The "less than or equal to" symbol (≤) is used for 320 because Rolando can drive exactly 320 miles over 8 weeks.
- The "less than" symbol (<) is used for 480 because Rolando drives less than 60 miles per week, thus less than 480 miles in total.
**C. Modeling Gas Expenses with Inequality**
Rolando buys between 8.5 and 11 gallons of gas each week, with prices ranging from $2.40 to $2.65 per gallon. To model his possible weekly spending:
Let \( g \) be the gallons of gas bought and \( p \) the price per gallon. Then:
\[ 2.40 \times 8.5 \leq m \leq 2.65 \times 11 \]
\[ 20.40 \leq m \leq 29.15 \]
Thus, the inequality captures all possible amounts of money \( m \) Rolando spends on gas each week.
**Conclusion**
Through understanding and using inequalities, we can effectively capture the range of Rolando's driving distances and potential gas expenses over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2df48705-4238-4207-b57b-19ed7b40517e%2Fea7e3469-86a8-413f-a837-db9fc4799d58%2Fnxg6y4h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Rolando's Driving and Gas Usage: Exploring Compound Inequalities**
Rolando drives at least 40 miles but less than 60 miles each week. Let's explore the ways we can represent and interpret this information using inequalities and analyze his potential spending on gas.
**A. Graphing the Compound Inequality**
To represent all possible distances Rolando could drive over 8 weeks, use the compound inequality for weekly driving:
- Minimum distance: 40 miles/week
- Maximum distance: less than 60 miles/week
For 8 weeks, the total distance range is:
\[ 40 \times 8 \leq x < 60 \times 8 \]
\[ 320 \leq x < 480 \]
On the number line, the graph is a segment starting from 320 and ending before 480, indicating that the total distance driven ranges from 320 to just under 480 miles.
**Graph Explanation:**
The number line marks increments of 40 miles, from 40 to 600 miles. The range of interest where Rolando might drive is highlighted from 320 to just under 480 miles, representing possible total driving distances for 8 weeks.
**B. Explanation of Symbols for Endpoints**
In the compound inequality \( 320 \leq x < 480 \):
- The "less than or equal to" symbol (≤) is used for 320 because Rolando can drive exactly 320 miles over 8 weeks.
- The "less than" symbol (<) is used for 480 because Rolando drives less than 60 miles per week, thus less than 480 miles in total.
**C. Modeling Gas Expenses with Inequality**
Rolando buys between 8.5 and 11 gallons of gas each week, with prices ranging from $2.40 to $2.65 per gallon. To model his possible weekly spending:
Let \( g \) be the gallons of gas bought and \( p \) the price per gallon. Then:
\[ 2.40 \times 8.5 \leq m \leq 2.65 \times 11 \]
\[ 20.40 \leq m \leq 29.15 \]
Thus, the inequality captures all possible amounts of money \( m \) Rolando spends on gas each week.
**Conclusion**
Through understanding and using inequalities, we can effectively capture the range of Rolando's driving distances and potential gas expenses over time.
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