Help please and can provide correct answer ### 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. $567.00B. $680.40C. $648.00D. $793.80### Explanation of Chain DiscountsA 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**### SummaryThe 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.

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? B. $680.40 A. $567.00 C. $648.00 D. $793.80

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? B. $680.40 A. $567.00 C. $648.00 D. $793.80

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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Question

Help please and can provide correct answer

### 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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