Question

a manufacturer introduces a new high - speed digital press that can be used to print brochures, business cards, posters, and photos at a list price of $120,800. find the net cost if a trade discount of 5/24/5 is given on the first ten sold. the net cost is $\square$. (round to the nearest cent as needed.)

Explanation:

Step1: Understand the trade discount series

A trade discount of \(5/24/5\) means we apply three successive discounts: first \(5\%\), then \(24\%\), then \(5\%\). To find the net cost, we first find the complement of each discount rate (i.e., \(1 - \text{discount rate}\)) and then multiply them together with the list price.

The complement of \(5\%\) (or \(0.05\)) is \(1 - 0.05= 0.95\).

The complement of \(24\%\) (or \(0.24\)) is \(1 - 0.24 = 0.76\).

The complement of \(5\%\) (or \(0.05\)) is \(1 - 0.05 = 0.95\).

Step2: Calculate the net cost factor

The net cost factor is the product of the three complements. So we calculate:

\(0.95\times0.76\times0.95\)

First, calculate \(0.95\times0.76\):

\(0.95\times0.76 = 0.722\)

Then, multiply the result by \(0.95\):

\(0.722\times0.95=0.6859\)

Step3: Calculate the net cost

The list price is \(\$120,800\). To find the net cost, we multiply the list price by the net cost factor:

\(\text{Net Cost}=120800\times0.6859\)

\(120800\times0.6859 = 120800\times0.6859 = 82856.72\)

Answer:

\(82856.72\)