Algebra.Com's Answer #147206 by Edwin McCravy(20060)![\"\"](\"/images/stars/stars-13.gif\")  
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Edwin's answer:
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document.write( "SUPPOSE YOU ARE BUILDING A STORAGE BOX OF VOLUME 4368 in3. The length of the box will be 24 in. The height of the box will be 1 in more than its width, Find the height and the width.\r
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document.write( "I know v=lwh\r
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document.write( "v=4368in3
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document.write( "l=24
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document.write( "w=x
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document.write( "h=x+1\r
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document.write( "(24)(x)(x + 1) = 4368in3\r
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document.write( "(24 + x)(x + 1) = 4368in3\r
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document.write( "The inches cubed is confusing me because I know I have to factor and substitute 0 to solve for x but I am lost on this one.
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document.write( "Your first equation is correct but the second one is wrong.\r\n" );
document.write( "It should be 24x not (24 + x), you're multiplying 24 by x. You're\r\n" );
document.write( "not adding them.\r\n" );
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document.write( "Maybe this will help with your \"inch cubed\" confusion:\r\n" );
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document.write( "Below is one INCH, its LENGTH is 1 inch raised to the\r\n" );
document.write( "1 power. You can think of it as 1 INCH1.\r\n" );
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document.write( " \r\n" );
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document.write( "Below is one SQUARE INCH, its AREA is found by \r\n" );
document.write( "multiplying 1 inch length by 1 inch width, which is 1 \r\n" );
document.write( "INCH SQUARED, or 1 INCH2, or 1 SQUARE INCH.\r\n" );
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document.write( "Below is one CUBIC INCH, its VOLUME is found by \r\n" );
document.write( "multiplying 1 inch length by 1 inch width by 1 inch \r\n" );
document.write( "height, which is 1 INCH CUBED, or 1 INCH3.\r\n" );
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document.write( "What you really have in your first equation is:\r\n" );
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document.write( "(24 in)(x in)(x + 1 in) = 4368 in3\r\n" );
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document.write( "See the three \" in \" factors on the left? A unit of length,\r\n" );
document.write( "such as an inch, is just like a number. It can be raised to powers \r\n" );
document.write( "the same as numbers can.\r\n" );
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document.write( "When you raise an inch to the first power, you have a measurement of\r\n" );
document.write( "LENGTH.\r\n" );
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document.write( "When you raise an inch to the second power, you have a measurement of\r\n" );
document.write( "AREA.\r\n" );
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document.write( "When you raise an inch to the third power, you have a measurement of\r\n" );
document.write( "VOLUME.\r\n" );
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document.write( "You can start by putting all the inches in your equation on both\r\n" );
document.write( "sides like this:\r\n" );
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document.write( "(24 in)(x in)(x + 1 in) = 4368in 3\r\n" );
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document.write( "Then the inches on the left side are multiplied three times, so\r\n" );
document.write( "we can write the left side as \r\n" );
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document.write( "(24)(x)(x + 1)in3 = 4368in3\r\n" );
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document.write( "Now you can divide both sides by in3, and you\r\n" );
document.write( "just have the equation:\r\n" );
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document.write( "(24)(x)(x + 1) = 4368 with no inches in it at all.\r\n" );
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document.write( "Lets write (24)(x) as 24x, OK?\r\n" );
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document.write( "24x(x + 1) = 4368\r\n" );
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document.write( "We could go ahead and distribute, but what we should do \r\n" );
document.write( "to make things easier instead is to divide both sides by 24,\r\n" );
document.write( "since 4368 can be divided by 24 to give 182, so we have:\r\n" );
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document.write( "x(x + 1) = 182\r\n" );
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document.write( "Now you distribute:\r\n" );
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document.write( "x2 + x = 182\r\n" );
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document.write( "Get 0 on the right by subtracting 182\r\n" );
document.write( "from both sides:\r\n" );
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document.write( "x2 + x - 182 = 0\r\n" );
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document.write( "To factor that we have to think of a pair\r\n" );
document.write( "of inegers that have product 182 and difference 1.\r\n" );
document.write( "So they will have to be very near the square root\r\n" );
document.write( "of 182. The square root of 182 is 13.49073756,\r\n" );
document.write( "so the two closest integers to that are 13 and 14.\r\n" );
document.write( "And they do differ by 1 and have product 182.\r\n" );
document.write( "So we factor it this way:\r\n" );
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document.write( "(x - 13)(x + 14) = 0\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "x - 13 = 0\r\n" );
document.write( " x = 13\r\n" );
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document.write( "x + 14 = 0\r\n" );
document.write( " x = -14\r\n" );
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document.write( "We discard the negative answer. So the width is x inches\r\n" );
document.write( "or 13 inches, and the height is x + 1 or 13 + 1 or 14 inches.\r\n" );
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document.write( "Edwin \n" );
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