Question

a supplier offers a series discount of 8/22. find the net cost equivalent and the single discount equivalent.

the net cost equivalent is
(round to four decimal places as needed.)

the single discount equivalent is
(round to two decimal places as needed.)

Explanation:

Step1: Calculate net cost equivalent

A series discount of \(8/22\) means first a \(8\%\) discount, then a \(22\%\) discount. To find the net cost equivalent, we use the formula: \((1 - d_1)(1 - d_2)\), where \(d_1 = 0.08\) and \(d_2 = 0.22\).
First, calculate \(1 - d_1 = 1 - 0.08 = 0.92\).
Then, calculate \(1 - d_2 = 1 - 0.22 = 0.78\).
Multiply these two results: \(0.92\times0.78 = 0.7176\).

Step2: Calculate single discount equivalent

The single discount equivalent is \(1 - \text{net cost equivalent}\).
We know the net cost equivalent is \(0.7176\), so \(1 - 0.7176 = 0.2824\), which is \(28.24\%\) when converted to a percentage.

Answer:

The net cost equivalent is \(0.7176\).
The single discount equivalent is \(28.24\%\).