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### 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

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
|----------------------180 years ---------------------|
|---- 30 years ------|             |----- 43 years----|
Alfred        George
dies          born

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

Alfred                                                George
born                                                  dies
|----------------------180 years ---------------------|
|---- 40 years ------|             |----- 33 years----|
Alfred        George
dies          born

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/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

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