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### How much is the dagger worth?

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Date: 10/12/96 at 10:54:19
From: Gordon Miller
Subject: Sword and dagger

In one of my fighting fantasy books I can't answer a question. It
reads: The sword and dagger that you see are together worth 300 copper
pieces. The sword is worth 200 copper pieces more than the dagger.
How much is the dagger worth?

Alex Bon-Miller
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Date: 10/12/96 at 14:17:25
From: Doctor Mike
Subject: Re: Sword and dagger

Hi Alex,

Brilliant!  Fantasy books are getting into Algebra now.  Tell your
local school board that, and maybe they will buy some of these books
for the math section of the school library.

Let's say that the sword is worth S copper pieces and the dagger is
worth D copper pieces. The first fact you are told is that  S+D=300 .
Also you're told that  S=D+200 . Do you see how I translated the
English sentences into math equations? Now here is a secret factoid
known only to Algebra insiders. The equation S=D+200 tells you that
wherever you see S you can automatically substitute in D+200 and
nobody will know the difference. That is what an equation is:
something that tells you that two seemingly different things are in
reality exactly the same. So, back to the story....

When you substitute D+200 in for S in the first equation  S+D=300,
you get  (D+200)+D=300.  This is the same as  D+D+200=300  since as
everybody knows, you can add things up in any order you want.  [If
I'm going too slow for you and you already know all this stuff feel

Since D+D is the same as 2 times D , I'll just re-write that as 2*D to
get 2*D+200=300 .  I'm going to subtract 200 from both sides of the
equation to get  2*D=100 .  I can do that in an equation since,
remember, the two things on either side of the "= sign" are just two
names for the same thing.  Okay?

Now, back to the story. The equation 2*D=100 just says that "double
the value of the dagger is 100 copper pieces". You don't have to be a
rocket scientist to figure out from that that the dagger is worth 50
copper pieces. We also know that the sword is worth 200 more than
that, or 250 copper pieces.  Done!

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Middle School Algebra
Middle School Word Problems

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