Use the trade discount system shown in the table to calculate the cost of 800 lbs of product if the retail price is $6 per pound.
| | |
| :-------- | :---------------- |
| Trade Discount | |
| 0-100 lbs | 10% |
| 101-400 lbs | 20% |
| 401+ lbs | 40% |
Answer (2)
Calculate the cost for the first 100 lbs with a 10% discount: $100 \tims 6 \tims 0.9 = 540 .
Calculate the cost for the next 300 lbs with a 20% discount: $300 \tims 6 \tims 0.8 = 1440 .
Calculate the cost for the remaining 400 lbs with a 40% discount: $400 \tims 6 \tims 0.6 = 1440 .
Sum the costs to find the total cost: $540 + $1440 + 1440 = \boxed{3420}$.
Explanation
Problem Analysis We are given a trade discount system and asked to calculate the total cost of 800 lbs of a product with a retail price of $6 per pound, considering the different discount tiers based on quantity.
Calculating Cost for 0-100 lbs First, we calculate the cost for the first 100 lbs, which has a 10% discount. The cost per pound is $6, so the discounted price per pound is $6 * (1 - 0.10) = $6 * 0.9 = $5.40. Therefore, the cost for the first 100 lbs is 100 * $5.40 = $540.
Calculating Cost for 101-400 lbs Next, we calculate the cost for the next 300 lbs (from 101 to 400 lbs), which has a 20% discount. The discounted price per pound is $6 * (1 - 0.20) = $6 * 0.8 = $4.80. Therefore, the cost for these 300 lbs is 300 * $4.80 = $1440.
Calculating Cost for 401+ lbs Then, we calculate the cost for the remaining 400 lbs (from 401 to 800 lbs), which has a 40% discount. The discounted price per pound is $6 * (1 - 0.40) = $6 * 0.6 = $3.60. Therefore, the cost for these 400 lbs is 400 * $3.60 = $1440.
Calculating 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 the product, considering the trade discounts, is 3420 .
Examples
Imagine you're buying ingredients for a large bakery. Different quantities of flour, sugar, and chocolate have tiered discounts. Calculating the total cost involves applying these discounts to each ingredient's quantity, similar to the trade discount system. This ensures accurate budgeting and cost management for the bakery's operations. Understanding tiered discounts helps businesses optimize purchasing strategies and maximize profits.
The total cost for 800 lbs of a product priced at $6 per pound, applying the appropriate trade discounts, is $3420. This is calculated by breaking down the cost for each weight tier and summing them. The discount rates applied are based on the quantity of product purchased.
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