Question

after a series discount of 5/10/9, the net cost of a computer system is $897.41. what is the list price? the list price of the system is $\square. (round to the nearest cent as needed.)

Explanation:

Step1: Understand series discount

A series discount of 5/10/9 means we first apply a 5% discount, then a 10% discount on the result, and then a 9% discount on that new result. To find the net cost factor, we calculate the complement of each discount rate (1 - discount rate) and multiply them together.
The complement of 5% (0.05) is $1 - 0.05 = 0.95$.
The complement of 10% (0.10) is $1 - 0.10 = 0.90$.
The complement of 9% (0.09) is $1 - 0.09 = 0.91$.

Step2: Calculate net cost factor

Multiply the three complements together: $0.95\times0.90\times0.91$.
First, $0.95\times0.90 = 0.855$.
Then, $0.855\times0.91 = 0.77805$.

Step3: Find list price

Let $L$ be the list price. We know that the net cost (NC) is given by $NC = L\times$ net cost factor. We know $NC = 897.41$ and the net cost factor is $0.77805$. So we solve for $L$: $L=\frac{NC}{\text{net cost factor}}=\frac{897.41}{0.77805}$.
Calculating this division: $\frac{897.41}{0.77805}\approx1153.41$.

Answer:

\$1153.41