Another word problem

[Kyle Concannon]

Please help!
Three years ago. Pat was half as old as Duane. Seven years from now, Duane will be as many years older than Pat as Pat's age three years ago. How old is Duane now if he is 4 years older than Pat?

 

[Denis]

Please help!
Three years ago. Pat was half as old as Duane.
D - 3 = 2(P - 3)

Seven years from now, Duane will be as many years older than Pat as Pat's age three years ago.
D + 7 = P + 7 + P - 3

How old is Duane now if he is 4 years older than Pat?
All yours!

 

[soroban]

Hello, Kyle!

A very strange problem . . . Where did it come from?
This statement * is not needed!

Three years ago. Pat was half as old as Duane.
Seven years from now, Duane will be as many years older than Pat as Pat's age three years ago. *
How old is Duane now if he is 4 years older than Pat?

Let \(\displaystyle P\) = Pat's age now.
Let \(\displaystyle D\) = Duane's age now.

Three years ago, they were both three years younger.
. . Pat was \(\displaystyle P\,-\,3\) years old.
. . Duane was \(\displaystyle D\,-\,3\) years old.
Back then, Pat was half Duane's age: .\(\displaystyle P\,-\,3\:=\:\frac{1}{2}(D\,-\,3)\;\;\Rightarrow\;\;2P\,-\,D\:=\:3\) . [1]

We are told that Duane is 4 years old than Pat: .\(\displaystyle D\:=\\,+\,4\) . [2]

Solve the system of equations . . .