Use the trade discount system shown in the table to calculate the cost of 800 lbs of product if the retail price is $[tex]$6[/tex] per pound.
| Trade Discount |
| :----------------------------------: |
| 0-100 lbs | 10 % |
| 101-400 lbs | 20 % |
| 401+ lbs | 40 % |
$[?]
Answer (1)
Calculate the cost of the first 100 lbs with a 10% discount: $100 \times $6 \times 0.9 = 540 .
Calculate the cost of the next 300 lbs with a 20% discount: $300 \times $6 \times 0.8 = 1440 .
Calculate the cost of the remaining 400 lbs with a 40% discount: $400 \times $6 \times 0.6 = 1440 .
Sum the costs to find the total cost: $540 + $1440 + 1440 = \boxed{{$3420}}$.
Explanation
Understanding the Problem We are given a trade discount system based on the quantity of product purchased. The retail price is $6 per pound, and we need to calculate the total cost for 800 lbs of product. The discount varies depending on the quantity purchased: 10% for 0-100 lbs, 20% for 101-400 lbs, and 40% for 401+ lbs.
Calculating Cost for the First 100 lbs First, we calculate the cost for the first 100 lbs, which receives a 10% discount. The cost per pound is $6, so the discounted price per pound is $6 * (1 - 0.10) = $6 * 0.90 = $5.40. Therefore, the cost for the first 100 lbs is $100 * $5.40 = $540.
Calculating Cost for the Next 300 lbs Next, we calculate the cost for the next 300 lbs (from 101 lbs to 400 lbs), which receives a 20% discount. The cost per pound is $6, so the discounted price per pound is $6 * (1 - 0.20) = $6 * 0.80 = $4.80. Therefore, the cost for the next 300 lbs is $300 * $4.80 = $1440.
Calculating Cost for the Remaining 400 lbs Then, we calculate the cost for the remaining 400 lbs (from 401 lbs to 800 lbs), which receives a 40% discount. The cost per pound is $6, so the discounted price per pound is $6 * (1 - 0.40) = $6 * 0.60 = $3.60. Therefore, the cost for the remaining 400 lbs is $400 * $3.60 = $1440.
Calculating the Total Cost Finally, we sum the costs from the three ranges to find the total cost: $540 + $1440 + $1440 = $3420.
Final Answer Therefore, the total cost of 800 lbs of product, considering the trade discount system, is $3420 .
Examples
Trade discounts are commonly used in business to encourage larger purchases. For example, a store might offer discounts to customers who buy in bulk. This is similar to how a company might offer discounts to its employees for purchasing company products. Understanding how to calculate costs with trade discounts is essential for businesses to manage their pricing strategies and for consumers to understand the actual cost of goods when discounts are applied.
