document.write( "Question 198164: A Jewelery Box has a lenght that is 2 inches longer than the width and a height that is 1 inch smaller than the width. It has a volume of 140 cubic inches. What is the width?\r
\n" ); document.write( "\n" ); document.write( "Please please help. I appreciate it!\r
\n" ); document.write( "\n" ); document.write( "Thank you very much \n" ); document.write( "
Algebra.Com's Answer #148639 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
Edwin's solution:\r
\n" ); document.write( "\n" ); document.write( "A Jewelery Box has a length that is 2 inches longer than the width and a height that is 1 inch smaller than the width. It has a volume of 140 cubic inches. What is the width?
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Let the \"WIDTH=w\"\r\n" );
document.write( "

\n" ); document.write( ">>...length that is 2 inches longer than the width...<<
\n" ); document.write( "
\r\n" );
document.write( "So \"LENGTH+=+WIDTH+%2B+2\" or\r\n" );
document.write( "\r\n" );
document.write( "   \"LENGTH+=+w+%2B+2\"\r\n" );
document.write( "

\n" ); document.write( ">>...a height that is 1 inch smaller than the width...<<
\n" ); document.write( "
\r\n" );
document.write( "So \"HEIGHT+=+WIDTH+-+1\" or\r\n" );
document.write( "\r\n" );
document.write( "   \"HEIGHT+=+w+-+1\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The formula for volume is\r\n" );
document.write( "\r\n" );
document.write( "\"VOLUME=LENGTH%2AWIDTH%2AHEIGHT\"\r\n" );
document.write( "

\n" ); document.write( ">>...It has a volume of 140 cubic inches...<<
\n" ); document.write( "
\r\n" );
document.write( "So we substitute \"140\" for \"VOLUME\",\r\n" );
document.write( "\"w%2B2\" for \"LENGTH\", and \"w-1\" for \"HEIGHT\":\r\n" );
document.write( "\r\n" );
document.write( "\"140=%28w%2B2%29%2Aw%2A%28w-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "First we multiply the \"w\" by the \"%28w-1%29\"\r\n" );
document.write( "by distributing:\r\n" );
document.write( "\r\n" );
document.write( "\"140=%28w%2B2%29%2A%28w%5E2-w%29\"\r\n" );
document.write( "\r\n" );
document.write( "Now we use FOIL on the right:\r\n" );
document.write( "\r\n" );
document.write( "\"140=w%5E3-w%5E2%2B2w%5E2-2w\" \r\n" );
document.write( "\r\n" );
document.write( "\"140=w%5E3%2Bw%5E2-2w\"\r\n" );
document.write( "\r\n" );
document.write( "\"0=w%5E3%2Bw%5E2-2w-140\"\r\n" );
document.write( "\r\n" );
document.write( "\"w%5E3%2Bw%5E2-2w-140=0\"\r\n" );
document.write( "\r\n" );
document.write( "The possible roots of this equation are the\r\n" );
document.write( "factors of 140, which are\r\n" );
document.write( "\r\n" );
document.write( "±1, ±2, ±4, ±5, ±10, ±14, ±28, ±35, ±70, ±140  \r\n" );
document.write( "\r\n" );
document.write( "Start trying those with synthetic division and\r\n" );
document.write( "sooner or later you'll get around to trying\r\n" );
document.write( "x=5\r\n" );
document.write( "\r\n" );
document.write( "5 | 1  1 -2 -140\r\n" );
document.write( "  |    5 30  140\r\n" );
document.write( "  --------------\r\n" );
document.write( "    1  6 28    0\r\n" );
document.write( "\r\n" );
document.write( "So the polynomial has been factored as\r\n" );
document.write( "\r\n" );
document.write( "\"w%5E3%2Bw%5E2-2w-140=0\"\r\n" );
document.write( "\r\n" );
document.write( "has been factored as\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-5%29%28x%5E2%2B6x%2B28%29=0\"\r\n" );
document.write( "\r\n" );
document.write( "\"x-5-0\" so \"x=5\"\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2%2B6x%2B28=0\" just give imaginary solutions.\r\n" );
document.write( "\r\n" );
document.write( "So the \"WIDTH+=+w=5INCHES\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );