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.

It's easiest to start with real and work from there.

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 
about this some more, please write back.

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