Question

a bracelet had a net cost to a jeweler of $69.24 after a series trade discount of 12/18/12. find the list price to the jeweler.
the list price to the jeweler is $\square.
(round to the nearest cent as needed.)

Explanation:

Step1: Convert discounts to decimals

A 12% discount means we pay \(1 - 0.12 = 0.88\) of the price.
An 18% discount means we pay \(1 - 0.18 = 0.82\) of the price.
A 12% discount means we pay \(1 - 0.12 = 0.88\) of the price.

Step2: Multiply the decimal factors

We multiply these factors together to get the net cost factor: \(0.88\times0.82\times0.88\)
First, \(0.88\times0.82 = 0.7216\)
Then, \(0.7216\times0.88 = 0.635008\)

Step3: Solve for list price

Let \(L\) be the list price. We know that net cost \(= L\times\) net cost factor. So, \(69.24 = L\times0.635008\)
To find \(L\), we divide both sides by \(0.635008\): \(L=\frac{69.24}{0.635008}\approx109.04\)

Answer:

\(109.04\)