The list price of an item is​ $91.33. The supplier is offering a series trade discount of 18 divided by 11 divided by 19. Find the net cost.
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Part 1
The net cost of the item is ​$
  
enter your response here. 

To find the net cost of the item after applying a series of trade discounts, we follow these steps:

1. The list price is $91.33.
2. The series trade discounts are 18%, 11%, and 19%.

The net cost is calculated as follows:

\[
\text{Net cost} = \text{List price} \times (1 - d_1) \times (1 - d_2) \times (1 - d_3)
\]
where $ d_1 $, $ d_2 $, and $ d_3 $ are the discount rates in decimal form.

First, convert the discounts to decimals:
\[
d_1 = \frac{18}{100} = 0.18, \quad d_2 = \frac{11}{100} = 0.11, \quad d_3 = \frac{19}{100} = 0.19
\]

Now, let's calculate the net cost.

\[
\text{Net cost} = 91.33 \times (1 - 0.18) \times (1 - 0.11) \times (1 - 0.19)
\]

Let me calculate that for you.The net cost of the item, after applying the series trade discount, is approximately **$53.99**.

Do you need any further details or clarification?

Here are some related questions to consider:
1. How do different types of discounts affect the final price?
2. What is the difference between a single discount and a series of discounts?
3. How can you reverse the process to find the original price given the net cost?
4. What would be the net cost if the discounts were applied in a different order?
5. How does the application of compound discounts compare to applying a single equivalent discount?

**Tip:** When dealing with multiple discounts, remember that they apply consecutively, not additively.

The list price of an item is​ $91.33. The supplier is offering a series trade discount of 18 divided by 11 divided by 19. Find the net cost.

Learn how to calculate the net cost of an item priced at $91.33 after applying a series of trade discounts of 18%, 11%, and 19%. This step-by-step solution demonstrates the use of percentage calculations and shows how to apply multiple discounts consecutively. Suitable for Grades 9-12.

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