a manufacturer offers a 30/10 chain discount if the invoice subtotal is above $1,000. if the list price is…
a manufacturer offers a 30/10 chain discount if the invoice subtotal is above $1,000. if the list price is $140 per item, what is the total price of the first invoice that activates the chain discount? $? round to the nearest cent.
Answer
Explanation:
Step1: Determine the number of items to reach subtotal
The chain - discount is activated when the invoice subtotal is above $1000. Since the list price per item is $140, the number of items $n$ needed to reach the subtotal for the discount is $\lceil\frac{1000}{140}\rceil$. $n=\lceil\frac{1000}{140}\rceil=\lceil7.142857\rceil = 8$ (we take the ceiling value because we need to exceed $1000$).
Step2: Calculate the subtotal
The subtotal before discount for 8 items is $140\times8 = 1120$.
Step3: Apply the first discount
The first discount is 30%. The price after the first 30% discount is $P_1=(1 - 0.30)\times1120=0.70\times1120 = 784$.
Step4: Apply the second discount
The second discount is 10%. The price after the second 10% discount is $P=(1 - 0.10)\times784=0.90\times784 = 705.60$.
Answer:
$705.60$