Math Problem Statement

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

Solution

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:

Net cost=List price×(1d1)×(1d2)×(1d3)\text{Net cost} = \text{List price} \times (1 - d_1) \times (1 - d_2) \times (1 - d_3) where d1d_1, d2d_2, and d3d_3 are the discount rates in decimal form.

First, convert the discounts to decimals: d1=18100=0.18,d2=11100=0.11,d3=19100=0.19d_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.

Net cost=91.33×(10.18)×(10.11)×(10.19)\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.

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Math Problem Analysis

Mathematical Concepts

Percentage
Discount Calculation
Series Discount

Formulas

Net cost = List price × (1 - d1) × (1 - d2) × (1 - d3)

Theorems

Percentage Discount

Suitable Grade Level

Grades 9-12