A manufacturer offers a $35/15$ chain discount if the invoice subtotal is above $[tex]$1,000$[/tex]. If the list price is $[tex]$45$[/tex] per item, what is the total price of the first invoice that activates the chain discount? Round to the nearest cent.

In order to activate the chain discount of 35/15 , the student must sell a minimum of 23 items, which gives a subtotal of $1,035. After applying the 35% and 15% discounts sequentially, the total price comes to $571.84. Thus, the total price for the first invoice is $571.84.
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Answered by Anonymous | 2025-07-04

Determine the minimum number of items to exceed the $1000 threshold: 23 items.
Calculate the subtotal for 23 items: $23 \times $45 = 1035 .
Apply the chain discount of 35/15: $1035 \times 0.65 \times 0.85 = 571.8375 .
Round the final price to the nearest cent: $\boxed{ 571.84} .

Explanation

Determine the Number of Items First, we need to determine how many items must be sold to reach an invoice subtotal that exceeds the discount threshold of $1000. The list price per item is $45.

Calculate Minimum Items To find the minimum number of items, we divide the discount threshold by the price per item: 45 1000 ​ ≈ 22.22 . Since we can't sell a fraction of an item, we round up to the nearest whole number, which is 23 items.

Calculate Subtotal Now, we calculate the subtotal for 23 items: 23 × 45 = 1035 . This confirms that selling 23 items will activate the chain discount since the subtotal is $1035, which is greater than $1000.

Apply 35% Discount Next, we apply the chain discount of 35/15. This means we first apply a 35% discount and then a 15% discount on the resulting price. Applying the 35% discount: 1035 × ( 1 − 0.35 ) = 1035 × 0.65 = 672.75 .

Apply 15% Discount Now, we apply the 15% discount to the discounted price: 672.75 × ( 1 − 0.15 ) = 672.75 × 0.85 = 571.8375 .

Round to Nearest Cent Finally, we round the total price to the nearest cent: 571.8375 ≈ 571.84 . Therefore, the total price of the first invoice that activates the chain discount is $571.84.


Examples
Chain discounts are commonly used in retail and wholesale businesses. For example, a store might offer a 20/10 chain discount to encourage bulk purchases. If a customer buys enough items to reach a subtotal of $5000, they would first receive a 20% discount, reducing the price to $4000. Then, they would receive an additional 10% discount, further reducing the price to $3600. This strategy helps businesses increase sales volume while rewarding larger purchases.

Answered by GinnyAnswer | 2025-07-04