When Was King George Born?

Date: 08/23/2002 at 21:17:38
From: Jordyn Culbreth
Subject: Algebra

King George died 180 years after King Alfred was born. Their combined 
age when they died was 73 years. King Alfred died in 315 A.D. In what 
year was King George born?

Date: 08/26/2002 at 07:17:57
From: Doctor Ian
Subject: Re: Algebra

Hi Jordyn,

Let's try putting this information into a timeline:

  Alfred                                              George 
  born                                                dies
  |----------------------180 years -------------------|
  |---- A years ------|             |----- G years----|
                      Alfred        George
                      dies          born
                      (315 AD)      (? AD)

I'm not entirely sure what you mean when you say that "their 
combined age when they died was 73 years." Do you mean that

  A + G = 73

If so, then suppose Alfred lived to be 30 years old.  Then we have

  Alfred                                                George 
  born                                                  dies
  (285 AD)                                              (465 AD)
  |----------------------180 years ---------------------|
  |---- 30 years ------|             |----- 43 years----|
                       Alfred        George
                       dies          born
                       (315 AD)      (422 AD)

On the other hand, suppose Alfred lived to be 40 years old. Then we 
have 

  Alfred                                                George 
  born                                                  dies
  (275 AD)                                              (455 AD)
  |----------------------180 years ---------------------|
  |---- 40 years ------|             |----- 33 years----|
                       Alfred        George
                       dies          born
                       (315 AD)      (422 AD)

Now, this is kind of interesting! Could it just be a coincidence that 
both numbers give the same date? 

Suppose we pick any age for Alfred, and call it A.  Then George's age 
must be (73-A). If we know that Alfred died in 315, then

  Alfred dies:  315
  Alfred born:  315 - A
  George dies:  315 - A + 180
  George born:  315 - A + 180 - (73 - A)

What does this tell you about the year George was born? 

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