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Use the Delivery Charges information above to answer this question. Yaster Shipping, a competing package delivery service, charges a base price for overnight delivery of packages weighing 2 pounds or less and a surcharge for each additional pound (or fraction thereof). You are billed $27.20 for shipping a 5.3 pound package and $71.14 for shipping a 20.9 pound package. How much does it cost to ship a 50.9 pound package? $ Round to the nearest cent.

Use the Delivery Charges information above to answer this question. Yaster Shipping, a competing package delivery service, charges a base price for overnight delivery of packages weighing 2 pounds or less and a surcharge for each additional pound (or fraction thereof). You are billed $27.20 for shipping a 5.3 pound package and $71.14 for shipping a 20.9 pound package. How much does it cost to ship a 50.9 pound package? $ Round to the nearest cent.

Advanced Engineering Mathematics
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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### Delivery Charges Many package delivery services charge a **base price** for packages up to some weight and a **surcharge** for each additional pound (or fraction thereof). In this context: - **Base price** refers to the initial fee charged for the delivery of a package up to a specified weight limit. - **Surcharge** indicates an additional fee imposed for each pound (or part of a pound) over the specified weight limit. Understanding these terms is essential for accurately calculating the total cost of package delivery services. This information can typically be used to estimate shipping costs effectively, especially for businesses and individuals who regularly send packages.
Transcribed Image Text:### Delivery Charges Many package delivery services charge a **base price** for packages up to some weight and a **surcharge** for each additional pound (or fraction thereof). In this context: - **Base price** refers to the initial fee charged for the delivery of a package up to a specified weight limit. - **Surcharge** indicates an additional fee imposed for each pound (or part of a pound) over the specified weight limit. Understanding these terms is essential for accurately calculating the total cost of package delivery services. This information can typically be used to estimate shipping costs effectively, especially for businesses and individuals who regularly send packages.
### Determining Shipping Costs with Yaster Shipping **Problem Statement:** Use the Delivery Charges information provided above to answer this question. Yaster Shipping, a competing package delivery service, charges a base price for overnight delivery of packages weighing 2 pounds or less and a surcharge for each additional pound (or fraction thereof). You are billed $27.20 for shipping a 5.3 pound package and $71.14 for shipping a 20.9 pound package. How much does it cost to ship a 50.9 pound package? $ ____________. Round to the nearest cent. **Explanation for Educators:** This problem involves understanding how a shipping company charges for delivering packages based on their weight. By analyzing the given charges for specific package weights, students can deduce the base price and the surcharge per additional pound. The students then apply this information to calculate the cost of shipping a package of a different weight. ### Analytical Breakdown: 1. **Identify Known Values:** - Cost for 5.3 pound package = $27.20 - Cost for 20.9 pound package = $71.14 2. **Set Up Equations:** - Let \( B \) = base price for package weighing 2 pounds or less - Let \( S \) = surcharge per additional pound (or fraction thereof) For the 5.3 pound package: \( B + S \times (5.3 - 2) = 27.20 \) For the 20.9 pound package: \( B + S \times (20.9 - 2) = 71.14 \) 3. **Solve the Equations:** - Solve for \(B\) and \(S\) using the system of linear equations formed by the two given costs. 4. **Apply Formula:** - Use the derived values of \(B\) and \(S\) to calculate the shipping cost for a 50.9 pound package: \( B + S \times (50.9 - 2) \) 5. **Calculation Result:** - Perform the arithmetic to determine the final cost, rounded to the nearest cent. **Note:** Understanding such practical applications of mathematics helps students engage with real-world problems and enhances their problem-solving skills. Encourage students to follow the step-by-step process and verify their calculations.
Transcribed Image Text:### Determining Shipping Costs with Yaster Shipping **Problem Statement:** Use the Delivery Charges information provided above to answer this question. Yaster Shipping, a competing package delivery service, charges a base price for overnight delivery of packages weighing 2 pounds or less and a surcharge for each additional pound (or fraction thereof). You are billed $27.20 for shipping a 5.3 pound package and $71.14 for shipping a 20.9 pound package. How much does it cost to ship a 50.9 pound package? $ ____________. Round to the nearest cent. **Explanation for Educators:** This problem involves understanding how a shipping company charges for delivering packages based on their weight. By analyzing the given charges for specific package weights, students can deduce the base price and the surcharge per additional pound. The students then apply this information to calculate the cost of shipping a package of a different weight. ### Analytical Breakdown: 1. **Identify Known Values:** - Cost for 5.3 pound package = $27.20 - Cost for 20.9 pound package = $71.14 2. **Set Up Equations:** - Let \( B \) = base price for package weighing 2 pounds or less - Let \( S \) = surcharge per additional pound (or fraction thereof) For the 5.3 pound package: \( B + S \times (5.3 - 2) = 27.20 \) For the 20.9 pound package: \( B + S \times (20.9 - 2) = 71.14 \) 3. **Solve the Equations:** - Solve for \(B\) and \(S\) using the system of linear equations formed by the two given costs. 4. **Apply Formula:** - Use the derived values of \(B\) and \(S\) to calculate the shipping cost for a 50.9 pound package: \( B + S \times (50.9 - 2) \) 5. **Calculation Result:** - Perform the arithmetic to determine the final cost, rounded to the nearest cent. **Note:** Understanding such practical applications of mathematics helps students engage with real-world problems and enhances their problem-solving skills. Encourage students to follow the step-by-step process and verify their calculations.
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