Using complements (with respect to 1) of the single discounts, find the net cost equivalent for the following discount.
-
A)0.65
B)0.35
C)0.478125
D)0.521875

Question

Using complements (with respect to 1) of the single discounts, find the net cost equivalent for the following discount.
-
A)0.65 
B)0.35 
C)0.478125 
D)0.521875

Quizplus · Accepted Answer

To find the net cost equivalent, we need to use the formula:
Net Cost Equivalent = 1 - (Complement of First Discount)*(Complement of Second Discount)*...

Here, the given discount is 35%. Let's find the complement of this discount with respect to 1:
Complement of 35% discount = 1 - 0.35 = 0.65

Therefore, the net cost equivalent would be:
Net Cost Equivalent = 1 - (0.65) = 0.35

Hence, the best choice is C, which matches with the calculated value. The complement of a discount is the percentage of the original price that is paid after the discount is subtracted.

For example, if a shirt is originally $20 and there is a 25% discount, the complement of the discount is 75%, meaning that the customer pays 75% of the original price ($15).

Using this concept, we can find the net cost equivalent of the given discount.

The single discount is not specified, so let's assume it is x%.

The complement of the discount is 100% - x%.

If the net cost equivalent is y, we can set up the equation:

(100% - x%) = y/1

Solving for x%, we get:

x% = 100% - y

Now, plugging in the numbers given in the answer choices, we get:

A) x% = 100% - 0.65 = 99.35% 
B) x% = 100% - 0.35 = 99.65% 
C) x% = 100% - 0.478125 = 99.521875% 
D) x% = 100% - 0.521875 = 99.478125%

We want the discount percentage to be as high as possible (i.e. the complement to be as low as possible) in order to get the best deal. Therefore, we choose the answer choice with the lowest complement, which is C.

Note: The net cost equivalent can also be found directly by using the formula:

Net cost equivalent = (original price) * (1 - combined discount percentage)

However, since only one discount percentage is given, we need to use complements to find the equivalent for that single discount.

Using Complements (With Respect to 1) of the Single Discounts