From Word Problems to Equations

Date: 01/28/99 at 22:46:54
From: Jeannie Weismann
Subject: Algebra

My daughter has come to me to get help in translating to an equation 
and solving the following problem:

If the sides of a square are lengthened by 7 inches, the area becomes 
121 inches squared. Find the length of a side of the original square.

(I guessed the answer to be 4 but have no idea how to write the 
equation to solve the problem.) The problem before it has the answer in 
the back of the book, but shows no work, and we would like to know how 
to solve with showing work. That problem reads: If the sides of a 
square are lengthened by 3m, the area becomes 81m squared. Find the 
length of a side of the original square. The answer is 6. Please show 
me how to translate to an equation so I can help teach her how to do 
this. Thank you.

Date: 01/29/99 at 12:33:30
From: Doctor Peterson
Subject: Re: Algebra

Hi, Jeannie. Let's start with the preceding problem, and then I'll let 
you find your own solution.

If the sides of a square are lengthened by 3m, we can call the original 
side length S (meters), and the new sides are (S+3). The area is the 
square of the side length, so our equation is

    (S+3)^2 = 81

(We write ^2 for an exponent of 2.)

To solve this, we can take the square root of both sides to get

    S+3 = 9

Now we subtract 3 from both sides and get

    S = 6

Your problem is very similar, and your answer is right. It really 
doesn't take algebra to solve this one!

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