Selling the Bike

Date: 1 Mar 1995 07:42:34 -0500
From: Kathleen Stastny
Subject: Math

Billy bought a bike for $40 and sold it for $50. He plans to buy it back 
for $60 and sell it again for $70.  Will he make money, lose money, or 
come out even?  

I'm in 5th grade.

Thanks.

Date: Wed, 01 Mar 1995 15:54:49 -0500
From: Daniel Eisenbud
Subject: Re: Math

Well, one way to look at the problem is to add up how much money Billy
receives, and how much he pays.  He pays $40 for the bike the first time,
and $60 the second, making $100.  If you add up how much he gets each 
time he sells it, you'll see how much money he received.  If he took in 
more money than he payed, he'll come out ahead; if he payed more than he
received, he'll lose money.  Can you do the rest of the problem?  Feel
free to write back if you have any questions about this.

-Doctor Dan,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 8/27/96 at 22:34:25
From: BRUCE F HELLER
Subject: Profit on Selling, Buying Bike

Dear Dr. Math,

Billy bought a bike for $40 and sold it for $50. He plans to buy it 
back for $60 and sell it again for $70.  Will he make money, lose 
money, or come out even?  

I would like to become a mathematician or an engineer.  Do you 
think that I would be good at being a mathematician or an engineer 
(mainly mathematician)?

Problem Solver,
   Bryan "Theta" Heller

Date: 8/30/96 at 11:4:48
From: Doctor Jerry
Subject: Re: Profit on Selling, Buying Bike

One way of thinking about Billy is to write down what he has at 
various times.  Let's let the letter "s" represent a certain amount of 
money.

1. No bike and 40 + s dollars.
2. Bike and s dollars.
3. No bike and 50 + s dollars.
4. Bike and s - 10 dollars.
5. No bike and 60 + s dollars.

Comparing what Billy has at time 5 with what he had at time 1, it is 
clear that he made 20 dollars.  

If you enjoy solving problems you may very well become a good engineer 
or mathematician.  

One of the most famous mathematicians of this century, David Hilbert, 
was known not so much because he solved problems very fast, but 
because he could solve more kinds of problems than most other people.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/