An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the cost for the first 100 lbs with 0% discount: cos t 1 = 100 l b s × $2/ l b = $200 .
Calculate the cost for the next 300 lbs with 5% discount: cos t 2 = 300 l b s × $2/ l b × 0.95 = $570 .
Calculate the cost for the remaining 800 lbs with 15% discount: cos t 3 = 800 l b s × $2/ l b × 0.85 = $1360 .
Calculate the total cost: t o t a l c os t = cos t 1 + cos t 2 + cos t 3 = $2130 . The final cost is 2130 .
Explanation
Understanding the Discount System Let's break down the cost calculation based on the given trade discount system. We have three discount tiers to consider: 0-100 lbs at 0% discount, 101-400 lbs at 5% discount, and 401+ lbs at 15% discount. We need to calculate the cost for each tier and then sum them up to find the total cost for 1200 lbs of the product.
Calculating Cost for the First Tier First, we calculate the cost for the first 100 lbs, which has a 0% discount. The retail price is $2 per pound, so the cost for this tier is: cos t 1 = 100 l b s × $2/ l b = $200
Calculating Cost for the Second Tier Next, we calculate the cost for the next 300 lbs (from 101 lbs to 400 lbs), which has a 5% discount. The discounted price is 95% of the retail price (100% - 5% = 95%). So, the cost for this tier is: cos t 2 = 300 l b s × $2/ l b × ( 1 − 0.05 ) = 300 × 2 × 0.95 = $570
Calculating Cost for the Third Tier Now, we calculate the cost for the remaining 800 lbs (since we have 1200 lbs total, and we've already accounted for 100 + 300 = 400 lbs). This tier has a 15% discount. The discounted price is 85% of the retail price (100% - 15% = 85%). So, the cost for this tier is: cos t 3 = 800 l b s × $2/ l b × ( 1 − 0.15 ) = 800 × 2 × 0.85 = $1360
Calculating the Total Cost Finally, we sum up the costs from all three tiers to find the total cost: t o t a l c os t = cos t 1 + cos t 2 + cos t 3 = $200 + $570 + $1360 = $2130
Final Answer Therefore, the total cost for 1200 lbs of the product, considering the trade discount system, is $2130.
Examples
Trade discounts are commonly used in various industries to encourage larger purchases. For example, a bookstore might offer a 10% discount on orders between 50 and 100 books and a 15% discount on orders over 100 books. This encourages schools and libraries to buy in bulk. Understanding how to calculate these discounts helps businesses manage their pricing strategies and helps customers understand the true cost of their purchases.
The device delivers a total charge of 450 coulombs in 30 seconds. This charge corresponds to approximately 2.81 x 10^21 electrons flowing through the device. Therefore, around 2.81 quintillion electrons passed through the device in that time frame.
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