Use the trade discount system shown in the table to calculate the cost of 600 lbs of product if the retail price is $[tex]$3[/tex] per pound.
| | |
| :-------------------- | :----- |
| Trade Discount | |
| $0-100 lbs$ | $0 \%$ |
| $101-400 lbs$ | $5 \%$ |
| $401+ lbs$ | $15 \%$ |
Answer (2)
Calculate the cost of the first 100 lbs at retail price: 100 × $3 = $300 .
Calculate the cost of the next 300 lbs with a 5% discount: 300 × $3 × 0.95 = $855 .
Calculate the cost of the remaining 200 lbs with a 15% discount: 200 × $3 × 0.85 = $510 .
Calculate the total cost by summing the costs from each range: $300 + $855 + $510 = $1665 .
Explanation
Understanding the Problem We are given a trade discount system and asked to calculate the total cost of 600 lbs of a product that has a retail price of $3 per pound. The discount varies based on the quantity purchased.
Analyzing the Discount System The discount system is as follows:
0-100 lbs: 0% discount
101-400 lbs: 5% discount
401+ lbs: 15% discount
We need to calculate the cost for each range and sum them up to find the total cost.
Calculating Cost for the First 100 lbs First 100 lbs cost: 100 × $3 = $300
Calculating Cost for the Next 300 lbs Next 300 lbs (101-400 lbs) cost: The discount is 5%, so the price per pound is $3 \times (1 - 0.05) = $3 \times 0.95 = $2.85 The cost for these 300 lbs is: 300 × $2.85 = $855
Calculating Cost for the Remaining 200 lbs Remaining 200 lbs (401-600 lbs) cost: The discount is 15%, so the price per pound is $3 \times (1 - 0.15) = $3 \times 0.85 = $2.55 The cost for these 200 lbs is: 200 × $2.55 = $510
Calculating the Total Cost Total cost: T o t a l C os t = $300 + $855 + $510 = $1665
Final Answer Therefore, the total cost of 600 lbs of the product is $1665.
Examples
Trade discounts are commonly used by suppliers to encourage larger purchases from retailers. For example, a local bakery might offer a discount on flour purchases based on the quantity ordered. If a bakery orders 100 lbs of flour, they pay the full retail price. However, if they order between 101 and 400 lbs, they receive a 5% discount, and if they order more than 400 lbs, they receive a 15% discount. This incentivizes the bakery to order larger quantities, reducing the supplier's transaction costs and ensuring a steady demand for their product. Understanding how to calculate these discounts helps businesses manage their costs effectively and make informed purchasing decisions.
The total cost for 600 lbs of the product at a retail price of $3 per pound, considering the applicable trade discounts, is $1665. This cost is derived from various weight categories receiving full price or different percentage discounts. The calculations include segments for 100 lbs, 300 lbs, and the remaining 200 lbs, leading to the final total.
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