Fraction Equation Problem

Date: 10 May 1995 15:57:27 -0400
From: Dana Murray
Subject: Question 4

Good Morning Sir!

Thank you for the hint with Question 3.

Let 1/a = a + 1/b = b + 1/c = c + 1/d = 2.  

What is the value of abcd?

Thank you.

Date: 11 May 1995 10:29:18 -0400
From: Dr. Sydney
Subject: Re: Question 4

Dear Dana,

Hello!  I'll give you some hints on this problem, and then 
perhaps you can solve it for yourself.  First write out the 
problem as 4 equations:

1/a = 2
a + 1/b = 2
b + 1/c = 2
c + 1/d = 2

Now the problem looks easier.  The first equation is the 
easiest to solve.  Multiply both sides of the equation by 
a/2 to get :

1/2 = a

Now, plug this value for a into the second equation, so the 
second equation now becomes:

1/2 + 1/b = 2

Now, solve this equation as you did the first, and you will 
know what b is. Repeat this for the last 2 equations, and you 
will find out how much c and d are.  Now you can multiply these 
numbers together, and you will have the value of abcd!  If you 
have any questions about this, feel free to write back.

--Sydney, "dr.math"