document.write( "Question 60009: this problem is not from my textbook and i really need help since word problems are not my strongest...
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document.write( "The height of a rectangular box equals the length of an edge of a certain cube. The width of the box is 3 inches more than its height and the length of the box is 4 times its height. The volume of the box is 8 times the volume of the cube. Find the dimensions of the box and find the volume of the cube. \n" );
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Algebra.Com's Answer #41254 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! Write a simple equation for each sentence. \n" ); document.write( ": \n" ); document.write( "\"The height of a rectangular box equals the length of an edge of a certain cube\" \n" ); document.write( "Let x = height of the box, and x = dimension of the side of the cube \n" ); document.write( ": \n" ); document.write( " The width of the box is 3 inches more than its height \n" ); document.write( "width = (x+3) \n" ); document.write( ": \n" ); document.write( " and the length of the box is 4 times its height. \n" ); document.write( "Length = 4x \n" ); document.write( ": \n" ); document.write( " The volume of the box is 8 times the volume of the cube. \n" ); document.write( "Length * Width * Height = 8 times the vol of the cube \n" ); document.write( "4x * (x+3) * x = 8x^3 \n" ); document.write( ": \n" ); document.write( "Find the dimensions of the box and find the volume of the cube. \n" ); document.write( "If we find x we will know all. \n" ); document.write( ": \n" ); document.write( "4x * (x+3) * x = 8x^3 \n" ); document.write( ": \n" ); document.write( "4x^2(x+3) = 8x^3 \n" ); document.write( ": \n" ); document.write( "Divide both sides by 4x^2, resulting in: \n" ); document.write( " (x + 3) = 2x \n" ); document.write( ": \n" ); document.write( "x - 2x = -3 \n" ); document.write( ": \n" ); document.write( "-x = -3 \n" ); document.write( ": \n" ); document.write( "x = +3 is the height and the cube side size \n" ); document.write( ": \n" ); document.write( "Length = 4(3) = 12 \n" ); document.write( ": \n" ); document.write( "Width = (3 + 3) = 6 \n" ); document.write( ": \n" ); document.write( "Vol of the cube: 3^3 = 27 \n" ); document.write( ": \n" ); document.write( "Check to see if: 3*6*12 = 8*(3^3)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |