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 $126,900. find the net cost if a trade discount of 5/12/5 is given on the first ten sold. the net cost is $ (round to the nearest cent as needed.)

Explanation:

Step1: Understand trade discount series

A trade discount of \(5/12/5\) means we apply three successive discounts: \(5\%\), \(12\%\), and \(5\%\). First, convert each discount rate to a decimal. \(5\% = 0.05\), \(12\% = 0.12\), \(5\% = 0.05\). The complement of a discount rate \(d\) is \(1 - d\), which represents the portion of the price remaining after the discount.

Step2: Calculate complement of first discount

For the first discount of \(5\%\), the complement is \(1 - 0.05 = 0.95\).

Step3: Calculate complement of second discount

For the second discount of \(12\%\), the complement is \(1 - 0.12 = 0.88\).

Step4: Calculate complement of third discount

For the third discount of \(5\%\), the complement is \(1 - 0.05 = 0.95\).

Step5: Multiply the complements with the list price

The net cost is the list price multiplied by the product of the three complements. So, we calculate \(126900\times0.95\times0.88\times0.95\).

First, multiply \(0.95\times0.88 = 0.836\). Then, multiply \(0.836\times0.95 = 0.7942\). Now, multiply this by the list price: \(126900\times0.7942\).

\(126900\times0.7942 = 126900\times(0.7 + 0.09 + 0.004 + 0.0002)=126900\times0.7 + 126900\times0.09 + 126900\times0.004 + 126900\times0.0002\)

\(126900\times0.7 = 88830\), \(126900\times0.09 = 11421\), \(126900\times0.004 = 507.6\), \(126900\times0.0002 = 25.38\)

Adding these together: \(88830+11421 = 100251\), \(100251 + 507.6 = 100758.6\), \(100758.6+25.38 = 100783.98\)

Answer:

\(100783.98\)