document.write( "Question 1124151: The Bob's family room is 13 ft by 16 ft, and they want to carpet it, except for a border of uniform width. What would be the width of the border if they can afford only 108 sq ft of carpet? \n" ); document.write( "

Algebra.Com's Answer #740515 by ikleyn(52793) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "1. The easy way to solve it MENTALLY\r
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document.write( "The difference the length minus the width is  16 - 13 = 3 ft.\r\n" );
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document.write( "If the non-carpeted border is of uniform length, then the difference between the length and the width of the carpet \r\n" );
document.write( "    must be the same 3 ft.\r\n" );
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document.write( "So we need to find a decomposition of the number 108 (108 sq.ft., the area) into the product of two numbers with \r\n" );
document.write( "   the difference of 3 between them.\r\n" );
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document.write( "As soon as you re-formulated the problem in this way, you can guess the answer MENTALLY and MOMENTARILY: \r\n" );
document.write( "    the numbers are 12 and 9.\r\n" );
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document.write( "Answer.  The dimensions of the carpet are 12 and 9 feet.\r\n" );
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document.write( "         The uniform width of the border is 2 ft.  ( =  = . )\r\n" );
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\n" ); document.write( "\n" ); document.write( "2. Formal algebra solution\r
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document.write( "Let x be the uniform border width.\r\n" );
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document.write( "Then the dimensions of the carpet are (16-2x)  and  (13-2x) feet.\r\n" );
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document.write( "So the area of the carpet is\r\n" );
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document.write( "(16-2x)*(13-2x) = 108.\r\n" );
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document.write( "It is your equation to find the unknown x.\r\n" );
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document.write( "Simplify it; write as a quadratic equation in standard form and solve by using the quadratic formula or factoring.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see many other similar solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problems on the area and the dimensions of a rectangle surrounded by a strip\r
\n" ); document.write( "\n" ); document.write( "    - Cynthia Besch wants to buy a rug for a room \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Dimensions and the area of rectangles and circles and their elements\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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