Finding Age in an Algebra Word Problem

Date: 12/8/95 at 12:35:37
From: Anonymous
Subject: Word problem 

Doris is as much older than Joris as Joris is older than Boris.  
Five years ago Doris' age was double what the age difference 
between her and Joris will be 15 years from now.  How old 
is Boris?

We are stuck. I need help please.

Date: 1/20/96 at 13:20:7
From: Doctor Ethan
Subject: Re: Word problem 

Hey, neat problem,

The key here is to make a chart and set up your equations carefully.

I will help you make the chart and get the equations; then we will 
see if you can solve it.

Let d represent Doris's age now.
Let j represent Joris's age now,
and b represent Boris's age now.

So we know that 

d-j = j-b

That is from the first sentence.

And

d-5 = 2 ((d+15) - (j+15))

That is from the second sentence.

Now can you solve these equations?

I will help you simplify the second equation.

d - 5 = 2 (d+ 15 -j -15)

Do you see why?
It is because the - sign applies to both the j and the 15.  
Then we can simplify more to make it

d-5 = 2 (d-j)

Do you see why? (The fifteens cancel.)

So now we have two equations
d-j = j-b
d-5 = 2 (j-b)

Now see if you can solve them from there.

Good luck, and if you need more help write back.

- Doctor Ethan,  The Geometry Forum