Which one the following statements is true? 


Discount rate is a percent of the list price. 


Net price is the price which the manufacturer suggests an item be sold to the consumer. 


The net price equivalent rate for the chain discount 8/12 is less than the net price equivalent rate of the chain discount 12/8. 


A manufacturing store is offering 8% discount and additional 12% discount. The single equivalent discount rate offered by this store is 19% 



Let's go through each statement to determine which one is true:

### 1. **"Discount rate is a percent of the list price."**
- This statement is **true**. The discount rate is indeed a percentage of the list price (also known as the original price before any discounts are applied). The amount of discount is calculated by multiplying the list price by the discount rate.

### 2. **"Net price is the price which the manufacturer suggests an item be sold to the consumer."**
- This statement is **false**. The price suggested by the manufacturer for sale to the consumer is called the **suggested retail price (SRP)** or **manufacturer's suggested retail price (MSRP)**. The **net price** refers to the final price after all discounts and deductions have been applied.

### 3. **"The net price equivalent rate for the chain discount 8/12 is less than the net price equivalent rate of the chain discount 12/8."**
- This statement is **false**. Chain discounts are applied in sequence. The net price equivalent rate is calculated as the complement of each discount multiplied together. For 8/12:
  - \( 1 - 0.08 = 0.92 \)
  - \( 1 - 0.12 = 0.88 \)
  - Net price equivalent rate for 8/12 = \( 0.92 \times 0.88 = 0.8096 \)
  - Similarly, for 12/8, it also equals \( 0.8096 \), so the rates are equal, not less.

### 4. **"A manufacturing store is offering 8% discount and additional 12% discount. The single equivalent discount rate offered by this store is 19%."**
- This statement is **false**. When two successive discounts are applied, they don't simply add up. The formula for a single equivalent discount is:
  - \( 1 - (1 - \text{first discount}) \times (1 - \text{second discount}) \)
  - For 8% and 12%, it is:
    \[
    1 - (1 - 0.08) \times (1 - 0.12) = 1 - (0.92 \times 0.88) = 1 - 0.8096 = 0.1904 = 19.04\%
    \]
  - The correct equivalent discount is 19.04%, not 19%.

---

### Conclusion: The first statement **"Discount rate is a percent of the list price"** is the only true statement.

Would you like more details or have any questions?

Here are 5 related questions to expand the topic:
1. How is the net price calculated after a discount is applied?
2. What is the difference between a single discount and chain discounts?
3. How do you find the net price equivalent rate for a chain discount?
4. What is the formula for calculating successive discounts as a single equivalent discount?
5. How does the discount rate affect the profit margin?

**Tip:** When calculating successive discounts, always multiply their complements to find the net price or equivalent rate.

Which one of the following statements is true? Discount rate is a percent of the list price. Net price is the price which the manufacturer suggests an item be sold to the consumer. The net price equivalent rate for the chain discount 8/12 is less than the net price equivalent rate of the chain discount 12/8. A manufacturing store is offering 8% discount and additional 12% discount. The single equivalent discount rate offered by this store is 19%.

This problem explores the concepts of discount rates, net prices, and chain discounts. Learn how to calculate the net price equivalent rate and understand the difference between a single discount and chain discounts. The solution is detailed step by step, suitable for students in Grades 9-12.

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