How Much Does the Youngest Boy Get?

Date: 05/25/2000 at 19:33:55
From: Joshua
Subject: Word Problems

Five brothers, each born in a different year, share a gift of $100 
according to the following arrangement: each boy except the youngest 
gets $5 more than his next younger brother. How much does the youngest 
boy get?

Date: 05/26/2000 at 03:01:00
From: Doctor Jesse
Subject: Re: Word Problems

Hi, Josh.

The trick to most word problems is trying to turn the words into an 
equation. Once you have the equation, things are pretty easy (most of 
the time). Let's look at what we have. 

Five brothers are splitting $100... So, we could say something like:

     a + b + c + d + e = 100

But that doesn't do us much good on its own. We need to know how much 
the youngest boy got. But we have more information, which we can use 
to modify our equation. If the youngest boy is  a , and the next 
youngest is  b , etc., then we know that:

     b = a + 5
     c = b + 5
     d = c + 5
     e = d + 5

This gives us the ability to put everything in terms of  a  ...  b  is 
already that way:

     b = a + 5

Now, c = b + 5, or (a + 5) + 5, so c = a + 10. Get it? It is pretty 
easy to see that:

     d = a + 15
and

     e = a + 20

So now you can turn:

     a + b + c + d + e = 100

into:

     a + (a + 5) + (a + 10) + (a + 15) + (a + 20) = 100

And I'll let you take it from there... Good luck - you can do it.

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