Does Unit Price Always Give the Best Buy?

Date: 12/30/2007 at 07:34:12
From: Mitu
Subject: The four number operations (+,-, x , / )

Which is the better value/best buy?

13 videos cost $25.
11 videos cost $20.

How to find the better buy, because one is 13 videos and the other is 
11 videos, they are not the same number of videos.  If both deals were 
either 13 or 11 videos then it would be easier to find out because 
then you remove the cost of one video for both and then the one which 
is less is the cheaper one; but when the number of videos are 
different it becomes tough to compare.

I tried:

The 13 videos cost approximately $1.92 for one video.  And the 11 
videos cost approximately $1.82.  So 11 videos are better buy, but 
for $5 extra, you get 2 more videos, so which is the better buy?

I also tried:

For the 11 videos deal, you could get 5 videos for approximately 
$9.10, in the 13 videos deal you could get 5 videos for $9.60 
(approximately).  This shows 11 videos deal the cheaper one but I'm 
not sure.

Date: 12/30/2007 at 17:28:54
From: Doctor Rick
Subject: Re: The four number operations (+,-, x , / )

Hi, Mitu.

You are quite right: the 11 videos for $20 are a better buy, in terms 
of the price you're paying for each video.  I'm sure that is meant to 
be the answer to the problem.

You're also right to wonder whether this is the right way to judge 
the better buy.  In real life, your decision might depend on which 
videos you want!  We can't make a direct comparison between buying 11 
videos and buying 13 videos.

A better question might be:

Suppose you can buy any single video for $2.00, or any 11 videos for 
$20, or any 13 videos for $25.  Suppose further that there are 13 
videos that you want to buy.  Which of the following will be a better 
deal?

  (a) buying 13 videos at the individual price ($2.00 each)

  (b) buying 11 videos for $20 and the remaining two at $2.00 each

  (c) buying all 13 videos as a group at the $25 price

Do you see how this is a better question?  In each case you end up 
with the same 13 videos, so you can compare the results directly.

In everyday shopping, this issue shows up all the time.  I may be able 
to buy individual apples at 90 cents a pound, or a bag of 20 pounds of 
apples for $10.  If I buy the bag, I will pay a lot less per apple-- 
but what if I will only be able to eat 8 pounds of apples before they 
go bad?  Then I have effectively paid $10 for 8 pounds of apples, an 
average of $1.25 a pound.  That's not such a good deal!  (And I 
haven't even considered the fact that, when you buy apples by the bag, 
you don't get to select the better-looking apples.)  The price per 
pound is not the only thing to consider when judging the best deal.

However, if you CAN use as many apples as you can get, then the price 
per pound is a good measure of how good a buy you're getting.  If I'm 
buying bottled juice, let's say, and some comes in 64-ounce bottles 
while others come in 48-ounce bottles, I will check the unit price 
(the price per ounce in this case) to tell which is the better buy.  I 
don't need to buy a particular quantity; I'm fine with buying whatever 
quantity gives me the better deal.  Do videos work that way? Not for 
me.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 12/31/2007 at 04:47:27
From: Mitu
Subject: Thank you (The four number operations (+,-, x , / ))

Thank you Dr. Rick,
 
The Math question was a bit confusing and I am so grateful for your
help always.  I know I can rely on Dr. Math when I encounter such
problems.

Regards,

Mitu