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/ |
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