Strategy: Finding a Formula

Date: 11/14/97 at 09:43:43
From: Betsy 
Subject: Strategy: using a formula

Jill needs three pieces of lumber a total of 27 ft. long for a dog 
pen. The second piece has to be 4 ft. longer than the first, and the 
third piece has to be 4ft. longer than the second. How long is each 
piece of lumber?

Date: 11/25/97 at 11:46:38
From: Doctor Allan
Subject: Re: Strategy: using a formula

Hi Betsy,

You need to translate your word problem into math. I will give you a 
suggestion for how to proceed, and then you can see if this helps you
understand.

You have three pieces of lumber, whose total length is 27 ft. Let's 
call the length of the first piece of lumber x, the length of the 
second piece y, and the length of the third piece z. Since they add up 
to a total of 27 ft. we have:

   (1) x + y + z = 27

Do you understand this? Then we are told that the second piece of
lumber is 4 ft. longer than the first piece. This means that if we 
take the length of the first piece and add 4 ft. we will get the 
length of the second piece:

   (2) x + 4 = y

Finally we are told that the length of the third piece of lumber is 
4 ft. longer than the second piece. As before, this yields:

   (3) y + 4 = z

Now we have to do the math part. We need to find values for x, y and z 
such that the above equations become true statements. From equation 
(3) we get

   (4) y = z - 4

and since there is a y in equation 2 we can write z - 4 there instead. 
Equation (2) then becomes

       x + 4 = z - 4

But if we isolate x in this last equation we have

   (5) x = z - 8

Do you understand what I have done so far?

In (4) and (5) you have new expressions for x and y, and you should
substitute these into equation (1). Then you will find a value for z, 
and once you have this you can immediately find the values for y and z 
by putting your value for z into equations (4) and (5). 

Try to do this part yourself and let me know if you have problems.

Since x and y and z were the lengths of pieces 1, 2, and 3 you will 
have found the lengths once you have found the values for x, y and z.

I hope this helps.

-Doctor Allan,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/