Use the trade discount system shown in the table to calculate the cost of $1,000 lbs$ of product if the retail price is [tex]$4$[/tex] per pound.
| | |
|---|---|
| Trade Discount | |
| $0-100 lbs$ | $5 \%$ |
| $101-400 lbs$ | $15 \%$ |
| $401+ lbs$ | $30 \%$ |
Answer (2)
Determine the applicable discount rate: Since 401 lbs"> 1000 l b s > 401 l b s , the discount is 30% .
Calculate the total retail price: 1000 l b s × l b $4 = $4000 .
Calculate the discount amount: $4000 × 0.30 = $1200 .
Calculate the final cost: $4000 − $1200 = $2800 .
Explanation
Problem Analysis We are given a trade discount system and asked to calculate the cost of 1000 lbs of product. The retail price is $4 per pound. The discount varies based on the quantity purchased.
Determining the Discount The discount system is as follows:
0 − 100 lbs: 5% discount
101 − 400 lbs: 15% discount
401 + lbs: 30% discount
Since we are purchasing 1000 lbs, the applicable discount is 30% .
Calculating Total Retail Price First, calculate the total retail price without any discount: 1000 lbs × lb $4 = $4000
Calculating Discount Amount Next, calculate the discount amount: Discount Amount = Total Retail Price × Discount Rate = $4000 × 0.30 = $1200
Calculating Final Cost Finally, subtract the discount amount from the total retail price to find the final cost: Final Cost = Total Retail Price − Discount Amount = $4000 − $1200 = $2800 Therefore, the cost of 1000 lbs of product is $2800 .
Examples
Trade discounts are commonly used in business to encourage larger purchases. For example, a company might offer a discount to retailers who buy their products in bulk. This helps the company move more inventory and allows the retailer to increase their profit margin. Understanding how to calculate trade discounts is essential for businesses to accurately price their products and manage their finances. If a store buys 1000 items at a retail price of $5 each and receives a 20% discount, they would calculate their cost as follows: Total retail price: 1000 × $5 = $5000 . Discount amount: $5000 × 0.20 = $1000 . Final cost: $5000 − $1000 = $4000 .
To find the cost of 1,000 lbs of product, first determine the applicable discount of 30%, calculate the total retail price of $4,000, and subtract the discount of $1,200. This results in a final cost of $2,800. Thus, the cost of the product is $2,800 after applying the trade discount.
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