# Proving the Final Net Price with the Complement Method

## Introduction

The complement method can also be used with chain discounts as follows:
- First subtract each discount from 100 percent to find its complement.
- Then the complements is multiplied to find the percent, which represent the net price rate to be paid.
- The complement method can also be used to find the dollar amount of the discount.
- The single equivalent discount (SED), or the complement of the net-price rate is multiplied by the list price to find the discount.

SED = Complement of Net-Price Rate

Discount = List Price × SED

### Example: Find the final net price.

Zoho Appliances has a super freezer in stock it wants to clear out. The super freezers originally sold for
$1,185. Zoho Appliances is offering a discount of 25 percent less 15 percent, also written as 25/15.
What is the final net price of the super freezer?

- Find the complements. Complement of 25% is 75%. Complement of 15% is 85%.
- Find the net-price rate. Net Price Rate = Product of Complements of (Chain-Discount Rates) = 75% × 85% = 63.75%
- ind the net price. Net Price = List Price × Net-Price Rate = $1,185 × 63.75% = $755.44

### Practice: Find the net-price rate, the net price, the SED, and the discount.

Final Net Price
List Price | Chain Discounts | Net-Price Rate | Net Price | SED | Discount |

$950.00 | 25%/10% | ??? | ??? | ??? | ??? |

$1375.00 | 30%/20% | ??? | ??? | ??? | ??? |

$1975.00 | 20%/15% | ??? | ??? | ??? | ??? |

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Date of last modification: March 5, 2019