United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $24.80 for shipping a 3-pound package and $77.80 for a 23-pound package. Find the base price and the surcharge for each additional pound.
United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $24.80 for shipping a 3-pound package and $77.80 for a 23-pound package. Find the base price and the surcharge for each additional pound.
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
june 3 24
![### Problem Description:
**United Express Package Pricing**
United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). Here is the pricing information for two different packages:
- A customer is billed $24.80 for shipping a 3-pound package.
- A customer is billed $77.80 for a 23-pound package.
Your task is to find the base price and the surcharge for each additional pound.
### Steps to Solve:
1. **Define Variables:**
- Let the base price for a package weighing 1 pound or less be denoted by \( B \).
- Let the surcharge for each additional pound be denoted by \( S \).
2. **Set Up Equations:**
- For the 3-pound package: \( B + 2S = 24.80 \)
- For the 23-pound package: \( B + 22S = 77.80 \)
3. **Solve the System of Equations:**
- Using the method of elimination or substitution, solve for \( B \) and \( S \).
### Solution Method:
First, let's subtract the first equation from the second:
\[
(B + 22S) - (B + 2S) = 77.80 - 24.80
\]
This simplifies to:
\[
20S = 53.00
\]
\[
S = \frac{53.00}{20} = 2.65
\]
Now substitute \( S = 2.65 \) into the first equation:
\[
B + 2(2.65) = 24.80
\]
\[
B + 5.30 = 24.80
\]
\[
B = 24.80 - 5.30 = 19.50
\]
### Final Solution:
- **Base Price (B):** \$19.50
- **Surcharge per Additional Pound (S):** \$2.65
These values indicate that the base price for shipping a package weighing 1 pound or less is $19.50, and the surcharge for each additional pound (or fraction thereof) is $2.65.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90edbae4-cb8a-42ba-a96e-55296e00f27e%2F27af6620-4989-4fce-974c-9f319b1d2ea4%2Fmem51ve_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description:
**United Express Package Pricing**
United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). Here is the pricing information for two different packages:
- A customer is billed $24.80 for shipping a 3-pound package.
- A customer is billed $77.80 for a 23-pound package.
Your task is to find the base price and the surcharge for each additional pound.
### Steps to Solve:
1. **Define Variables:**
- Let the base price for a package weighing 1 pound or less be denoted by \( B \).
- Let the surcharge for each additional pound be denoted by \( S \).
2. **Set Up Equations:**
- For the 3-pound package: \( B + 2S = 24.80 \)
- For the 23-pound package: \( B + 22S = 77.80 \)
3. **Solve the System of Equations:**
- Using the method of elimination or substitution, solve for \( B \) and \( S \).
### Solution Method:
First, let's subtract the first equation from the second:
\[
(B + 22S) - (B + 2S) = 77.80 - 24.80
\]
This simplifies to:
\[
20S = 53.00
\]
\[
S = \frac{53.00}{20} = 2.65
\]
Now substitute \( S = 2.65 \) into the first equation:
\[
B + 2(2.65) = 24.80
\]
\[
B + 5.30 = 24.80
\]
\[
B = 24.80 - 5.30 = 19.50
\]
### Final Solution:
- **Base Price (B):** \$19.50
- **Surcharge per Additional Pound (S):** \$2.65
These values indicate that the base price for shipping a package weighing 1 pound or less is $19.50, and the surcharge for each additional pound (or fraction thereof) is $2.65.
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