a manufacturer offers a 45/10 chain discount if the invoice subtotal is above $1,000. if the list price is…

a manufacturer offers a 45/10 chain discount if the invoice subtotal is above $1,000. if the list price is $74 per item, what is the total price of the first invoice that activates the chain discount? $? round to the nearest cent.

a manufacturer offers a 45/10 chain discount if the invoice subtotal is above $1,000. if the list price is $74 per item, what is the total price of the first invoice that activates the chain discount? $? round to the nearest cent.

Answer

Explanation:

Step1: Calculate the number of items to reach subtotal

Since the chain - discount is activated when the invoice subtotal is above $1000 and the list price per item is $74, the number of items $n=\lceil\frac{1000}{74}\rceil$. $n = \lceil13.5135\rceil=14$ (using the ceiling function to ensure the subtotal is above $1000$).

Step2: Calculate the subtotal before discount

The subtotal before discount $S = 74\times14=1036$.

Step3: Apply the first - stage discount

The first discount is 45%. The price after the first discount $P_1=S\times(1 - 0.45)$. $P_1 = 1036\times0.55=569.8$.

Step4: Apply the second - stage discount

The second discount is 10%. The price after the second discount $P = P_1\times(1 - 0.1)$. $P=569.8\times0.9 = 512.82$.

Answer:

$512.82$