aster Shipping, a competing package delivery service, harges a base price for overnight delivery of packages veighing 2 pounds or less and a surcharge for each dditional pound (or fraction thereof). You are billed $33.28 for shipping a 5.2 pound package and $73.40 for hipping a 21.4 pound package. How much does it cost to
aster Shipping, a competing package delivery service, harges a base price for overnight delivery of packages veighing 2 pounds or less and a surcharge for each dditional pound (or fraction thereof). You are billed $33.28 for shipping a 5.2 pound package and $73.40 for hipping a 21.4 pound package. How much does it cost to
Chapter1: Equations, Inequalities, And Mathematical Modeling
Section1.3: Modeling With Linear Equations
Problem 3ECP: Your family has annual loan payments equal to 28 of its annual income. During theyear, the loan...
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Transcribed Image Text:**Yaster Shipping Cost Calculation**
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 $33.28 for shipping a 5.2 pound package and $73.40 for shipping a 21.4 pound package. How much does it cost to ship a 39.8 pound package?
**Task:**
Calculate the shipping cost for a 39.8-pound package and round your answer to the nearest cent.
**Step-by-Step Solution:**
1. **Identify the known costs and weights:**
- 5.2 pound package: $33.28
- 21.4 pound package: $73.40
2. **Determine the base price and surcharge fee:**
- Let B represent the base price for packages weighing 2 pounds or less.
- Let S represent the surcharge fee for each additional pound (or fraction thereof).
Based on the given information:
- \(33.28 = B + 3.2S\)
- \(73.40 = B + 19.4S\)
3. **Solve the system of equations:**
- From the first equation:
- \(B + 3.2S = 33.28\) ⇒ \(B = 33.28 - 3.2S\)
- Substitute \(B\) into the second equation:
- \(73.40 = (33.28 - 3.2S) + 19.4S\)
- \(73.40 = 33.28 + 19.4S - 3.2S\)
- \(73.40 = 33.28 + 16.2S\)
- \(73.40 - 33.28 = 16.2S\)
- \(40.12 = 16.2S\)
- \(S = \frac{40.12}{16.2}\)
- \(S ≈ 2.476\)
Using the value of \(S\) to find \(B\):
- \(B = 33.28 - 3.2 \times 2.476\)
- \(B = 33.28 - 7.9232\)
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