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.
| | |
| :-------- | :--------------- |
| 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 l b s × $6/ l b × ( 1 − 0.10 ) = $540 .
Calculate the cost for the next 300 lbs with a 20% discount: 300 l b s × $6/ l b × ( 1 − 0.20 ) = $1440 .
Calculate the cost for the remaining 400 lbs with a 40% discount: 400 l b s × $6/ l b × ( 1 − 0.40 ) = $1440 .
Calculate the total cost by summing the costs from each range: $540 + $1440 + $1440 = $3420 .
Explanation
Problem Analysis We need to calculate the total cost of 800 lbs of product with a retail price of $6 per pound, considering the trade discounts based on quantity. The discounts are 10% for 0-100 lbs, 20% for 101-400 lbs, and 40% for 401+ lbs.
Cost for the First 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 × 0.90 = $5.40 . Therefore, the cost for the first 100 lbs is 100 l b s × $5.40/ l b = $540 .
Cost for the Next 300 lbs Next, we calculate the cost for the next 300 lbs (from 101 lbs to 400 lbs), which has 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 l b s × $4.80/ l b = $1440 .
Cost for the Remaining 400 lbs Finally, we calculate the cost for the remaining 400 lbs (from 401 lbs to 800 lbs), which has 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 l b s × $3.60/ l b = $1440 .
Total Cost Calculation Now, we add the costs for each range to find the total cost: T o t a lC os t = $540 + $1440 + $1440 = $3420 .
Final Answer Therefore, the total cost for 800 lbs of product, considering the trade discounts, is $3420 .
Examples
Trade discounts are commonly used in various industries to incentivize larger purchases. For example, a construction company buying materials in bulk from a supplier might receive trade discounts based on the quantity of materials purchased. This helps the construction company reduce its costs and the supplier to increase its sales volume. Understanding how to calculate costs with trade discounts is essential for businesses to manage their finances effectively and make informed purchasing decisions.
The total cost for 800 lbs of product is calculated by applying trade discounts based on quantity. For the first 100 lbs, a 10% discount applies; for the next 300 lbs, a 20% discount; and for the last 400 lbs, a 40% discount. The final total after all discounts is $3420.
;
