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Facts

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1. Two regular polygons

2. Polygon A + Polygon B perimeter = 63 inches

   I. Can be written as the equation 

           3x + 6y = 63

              x ~~~> # of sides A

              y ~~~> # of sides B

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WHERE DID WE GET 6?

Let us eliminate some choices first, using the notes we have

A) Each side of figure B has a length of 6 inches.

    Isolating polygon B from the rest, focus!

    We have 6 * y, with y being the quantity of sides for polygon B. If y represents the sides quantity, I am going to assume that 6 represents the total length of each side, in inches. So I am in agreement with A.

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B) The number of sides from figure B is 6.

     I cannot say how many sides figure B has. THere is no provided picture, nor statistics inside the word problem.

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C) Each side of figure A has a length of 6 inches.

     I am satisfied with assuming that for figure A, with the quantity of sides in the figur eequal to x, the length of each side is the value of the coeffecient attached to the variable. For A, this is 3 inches. So I do not agree.

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D) The number of sides of figure A is 6.

   I cannot confirm this as true. It makes easy math and seems fit at first, but we have to investigate if we can take x * 3" + y * 6" and make any othe rcombinations be true.

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So for the suggested, with sides quanitty six and side length 3 inches, we shave off 18 inches to figure A. 

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         x = 6 sides

           = 3 in each

            = 18 inches

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That leaves us with 45 inches for figure B.

We are assuming, from reading the equation, that the length of the sides for figure B are 6 inches. 

We cannot divide 45 by 6 and result in a whole number qunatity of sides. Which is not realistic. 

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