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Part 1
An appliance has a list price of​ $21.76 and is offered to wholesalers with a series discount of 30 divided by 20 divided by 20. A retailer is offered the same appliance with a series discount of 30 divided by 20. Find the difference between the​ wholesalers' price and the​ retailer's price.
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Part 1
The difference between the two prices is ​$
  
enter your response here.

To solve this, let's break down both the wholesalers' and retailers' prices, based on their series discounts.

### Wholesalers' Price:
The appliance has a list price of **$21.76**, and the wholesalers are offered a **30%** discount, followed by a **20%** discount, and another **20%** discount.

1. **First discount of 30%**:
   \[
   21.76 \times (1 - 0.30) = 21.76 \times 0.70 = 15.232
   \]
   
2. **Second discount of 20%**:
   \[
   15.232 \times (1 - 0.20) = 15.232 \times 0.80 = 12.1856
   \]

3. **Third discount of 20%**:
   \[
   12.1856 \times (1 - 0.20) = 12.1856 \times 0.80 = 9.74848
   \]

So, the final price for the wholesaler is **$9.74848**.

### Retailers' Price:
The retailer is offered a **30%** discount followed by a **20%** discount.

1. **First discount of 30%**:
   \[
   21.76 \times (1 - 0.30) = 21.76 \times 0.70 = 15.232
   \]

2. **Second discount of 20%**:
   \[
   15.232 \times (1 - 0.20) = 15.232 \times 0.80 = 12.1856
   \]

So, the final price for the retailer is **$12.1856**.

### Difference Between Prices:
Now, let's find the difference between the wholesaler’s price and the retailer’s price:

\[
12.1856 - 9.74848 = 2.43712
\]

Thus, the difference between the wholesalers' price and the retailers' price is **$2.44**.

---

If you'd like further clarification or more details, feel free to ask. Here are some related questions you may find helpful:

1. How do you calculate the total price after applying multiple percentage discounts?
2. What is the formula for finding the final price with a series of percentage discounts?
3. How can you calculate the difference in pricing between multiple vendors using different discount structures?
4. What is the impact of larger or smaller discount percentages on the final price?
5. How can the order of applying discounts affect the final price?

**Tip:** Always apply discounts sequentially rather than calculating them all at once for series discount problems.

An appliance has a list price of​ $21.76 and is offered to wholesalers with a series discount of 30 divided by 20 divided by 20. A retailer is offered the same appliance with a series discount of 30 divided by 20. Find the difference between the​ wholesalers' price and the​ retailer's price.

Learn how to calculate the difference between wholesaler and retailer prices based on series discounts. This example uses a series discount of 30% × 20% × 20% for wholesalers and 30% × 20% for retailers, applied to an appliance priced at $21.76. Suitable for high school students (Grades 9-11).

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