Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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### Understanding Chain Discounts in Invoices **Problem Statement:** A manufacturer offers a 30/10 chain discount if the invoice subtotal is above $1,000. If the list price is $180 per item, what is the total price of the first invoice that activates the chain discount? **Options:** A. $567.00 B. $680.40 C. $648.00 D. $793.80 ### Explanation of Chain Discounts A chain discount, also known as a series discount, refers to multiple discounts applied one after another on the listed price of an item. In this problem, a 30/10 chain discount is given, meaning the first discount is 30%, and the second discount is an additional 10% on the already discounted price. ### Step-by-Step Calculation: 1. **Determine Total Quantity Needed:** - To activate the discount, the invoice subtotal must be over $1,000. - List price per item = $180 \( 180x > 1000 \) Solving for x: \( x > \frac{1000}{180} \approx 5.56 \) Thus, a minimum of 6 items are needed to qualify for the discount (since we can't have a fraction of an item). 2. **Calculate Initial Total:** \( 6 \times 180 = 1080 \) 3. **Apply First Discount (30%):** \( 1080 \times 0.70 = 756 \) (0.70 represents 100% - 30% = 70%) 4. **Apply Second Discount (10%):** \( 756 \times 0.90 = 680.40 \) (0.90 represents 100% - 10% = 90%) Hence, the total price of the first invoice that activates the chain discount is: **B. $680.40** ### Summary The correct answer is **B. $680.40**. This step-by-step approach illustrates how to apply a chain discount and ensure the calculation meets the stipulated conditions. Understanding this concept is essential for efficiently managing invoices and recognizing potential savings in bulk purchasing. --- ©2022 International Academy of Science. All Rights Reserved.
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Transcribed Image Text:### Understanding Chain Discounts in Invoices **Problem Statement:** A manufacturer offers a 30/10 chain discount if the invoice subtotal is above $1,000. If the list price is $180 per item, what is the total price of the first invoice that activates the chain discount? **Options:** A. $567.00 B. $680.40 C. $648.00 D. $793.80 ### Explanation of Chain Discounts A chain discount, also known as a series discount, refers to multiple discounts applied one after another on the listed price of an item. In this problem, a 30/10 chain discount is given, meaning the first discount is 30%, and the second discount is an additional 10% on the already discounted price. ### Step-by-Step Calculation: 1. **Determine Total Quantity Needed:** - To activate the discount, the invoice subtotal must be over $1,000. - List price per item = $180 \( 180x > 1000 \) Solving for x: \( x > \frac{1000}{180} \approx 5.56 \) Thus, a minimum of 6 items are needed to qualify for the discount (since we can't have a fraction of an item). 2. **Calculate Initial Total:** \( 6 \times 180 = 1080 \) 3. **Apply First Discount (30%):** \( 1080 \times 0.70 = 756 \) (0.70 represents 100% - 30% = 70%) 4. **Apply Second Discount (10%):** \( 756 \times 0.90 = 680.40 \) (0.90 represents 100% - 10% = 90%) Hence, the total price of the first invoice that activates the chain discount is: **B. $680.40** ### Summary The correct answer is **B. $680.40**. This step-by-step approach illustrates how to apply a chain discount and ensure the calculation meets the stipulated conditions. Understanding this concept is essential for efficiently managing invoices and recognizing potential savings in bulk purchasing. --- ©2022 International Academy of Science. All Rights Reserved.
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