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**Summary::**I have a document which was written by previous tutor supervisor/instructor at my undergraduate school. I want to learn how to use this technique for other math/physics subject besides algebra... I will provide an example of how to use this technique. I found an old textbook (College Algebra by Richard Heineman) with word problem on exercise 15 problem 1.

Dear Everyone,

*Disclaimer: I am not in school, or this is not a homework question for me. I am using an outdate math book (meaning no body in my knowledge is teaching out of this book) to learn this technique.*

Background information:

The Technique is using some transition words to help with solving words problems. Those words are (Let, then, But, so, Therefore). I believe this technique is kind prototype thinking of proof-writing for the pre-proof-writing classes (mainly, Pre-Calculus and Calculus, and not Geometry). I believe this technique will help with me in other situation like in differential equations, calculus, and other applied math fields. There is an example to illustrate this technique in the document:

"Suppose in designing a house, the living room is to be thrice as long as it is wide. The total area of the room is 507 square feet. What should be the length of the room?"

Solution to this example:

**Let**##w## be the width.

**Then**the length is ##3w##, and the area will be ##(3w)(w)=3w^2##.

**But**we know the total area is 507.

**So**##3w^2=507##. After we divide 3 and take the positive root on both side of the equation, we discovered ##w=13##.

**Therefore**(or any synonym), the length of the room is 39 feet because ##3 \cdot 13=39##.

This is the technique that I want to learn...

**So here is my problem:**

The difference of the squares of two consecutive integers is 43. Find the integers.

My work is the following:

"

**Let**##x## be an integer.

**Then**a consecutive integer is #x+1#, and the difference of the square of two consecutive integers is ##x^2-(x+1)^2##.

**But**we know that the difference is 43.

**So**##x^2-(x+1)^2=43##..."

I know the answer should be whatever ##x## is then ##x+1## will be next answer, also.

I think I have made a mistake on the algebraic expression; I don't know what is the error that I made.

Any help and/or suggestions will be appreciated.

Thanks,

cbarker1

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