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Comparing Individual Discounts to a Collective Discount

Date: 07/19/2005 at 07:33:52
From: Jay
Subject: collective Discount vs individual discounts

I am purchasing 2 books.  If each book carries a 10% discount, will it 
always be the same as a 10% discount on the total price of the 2 books?

Say Book A costs $100, Book B costs $100 and each has an 8% discount:

Book A after discount - $92
Book B after discount - $92
Total = $184

Original Sales Price of Book A + Book B = $200
Discount 8% on $200 = $200-$16 = $184

So it's the same.  I always thought individual discounts saved more 
money than collective discounts.

Date: 07/20/2005 at 05:01:16
From: Doctor Ian
Subject: Re: collective Discount vs individual discounts

Hi Jay,

Suppose the prices are A and B, and the discount is D.  Then if we 
discount the books individually, we get

   (A - AD) + (B - BD)

  = A - AD + B - BD

  = A + B - AD - BD

  = (A + B) - (AD + BD)

  = (A + B) - (A + B)D

Now let's apply the discount to both books at once:

    (A + B) - (A + B)D

It's the same, isn't it?  And we haven't even said what the prices or
discounts are.  So it must apply to any prices or discounts that we
could make up.

Does that make sense? 

- Doctor Ian, The Math Forum 

Date: 07/21/2005 at 03:35:32
From: Jay
Subject: Thank you (collective Discount vs individual discounts)

It makes sense.  Thanks very much, Dr. Ian.
Associated Topics:
Middle School Fractions
Middle School Number Sense/About Numbers

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