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### Story Problems: Real, Realistic, Theoretical

```Date: 10/24/2002 at 21:45:09
From: Jenifer Garner
Subject: Theoretical, realistic and real problems

I am trying to get the definitions for theoretical, realistic, and
real problems to be able to determine different types of story
problems.
```

```
Date: 10/25/2002 at 17:26:09
From: Doctor Achilles
Subject: Re: Theoretical, realistic and real problems

Hi Jenifer,

Thanks for writing to Dr. Math.

A real story problem is something that actually did happen or is
happening. For example, this morning I really had to be at work by
9:15 a.m. It really takes me 25 minutes to bike to work, 10 minutes to
eat breakfast, and 35 minutes to shower and get dressed. What time
should I have set my alarm for?

A realistic story problem is something that could happen, but did not
actually happen. For example, "Suzie went to the store and noticed
that there was a sale on 18-packs of eggs for \$3. The store also sells
individual eggs for \$0.25 each. She needs 14 eggs for a recipe, so any
eggs she buys over the 14 she needs will be wasted. Is it cheaper for
Suzie to buy one 18-pack or 14 individual eggs?" That problem is not
real because Suzie is just someone I made up and I also made up the
store, the eggs, the prices, and the recipe. But it is something that
COULD have happened, so it is REALISTIC.

A theoretical story problem is a little bit stranger. Here's an
example: "Normally, when Tom goes bowling, it takes 4 seconds from
when he throws the ball until it hits the pins. However, today there
is a wizard in the bowling alley. The wizard casts a spell on the
bowling ball so that it doesn't go at a constant speed any more, but
instead it goes like this: for the first second, the ball goes at its
normal speed, for the second second, it goes at half the normal speed,
for the third second, it goes at 1/8 the normal speed, for the fourth
second it goes at 1/16 its normal speed, and so on. It doesn't
accelerate; rather, it magically changes from one speed to a slower
speed every second. Under this magic spell, how long will it take a
ball Tom throws to reach the pins?" That problem is pure fantasy. Not
only is it NOT something that ever actually happened, it isn't even
something that ever COULD happen. So it isn't even realistic, it's
just plain theoretical.

I hope this helps. If you have other questions or you'd like to talk

- Doctor Achilles, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Definitions
Elementary Word Problems
Middle School Definitions
Middle School Word Problems

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