document.write( "Question 87072: it takes Mars 1.88 years to travel around the sun.It takes Mercury 0.24 years to orbit the sun. If the planets are in a straight line with the sun now, how long will it be before this is the case again? The answer must be accurate to the nearest hundredth of a year. \n" ); document.write( "
Algebra.Com's Answer #63043 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "it takes Mars 1.88 years to travel around the sun.It takes Mercury 0.24 years\r\n" );
document.write( "to orbit the sun. If the planets are in a straight line with the sun now, how\r\n" );
document.write( "long will it be before this is the case again? The answer must be accurate to\r\n" );
document.write( "the nearest hundredth of a year.\r\n" );
document.write( "\r\n" );
document.write( "We must find the smallest positive integer N \r\n" );
document.write( "such that when we multiply both 1.88 and .24 by N \r\n" );
document.write( "we get a positive integer, that is\r\n" );
document.write( "\r\n" );
document.write( "1.88N = P , whener P is a positive integer\r\n" );
document.write( " and\r\n" );
document.write( "\r\n" );
document.write( "0.24N = Q , whener Q is also a positive integer\r\n" );
document.write( "\r\n" );
document.write( "Multiply both equations by 100 to remove decimals:\r\n" );
document.write( "\r\n" );
document.write( "188N = 100P\r\n" );
document.write( "\r\n" );
document.write( "24N = 100Q\r\n" );
document.write( "\r\n" );
document.write( "Solve each for N\r\n" );
document.write( "\r\n" );
document.write( "N = \"100P%2F188\"\r\n" );
document.write( "\r\n" );
document.write( "N = \"25P%2F47\"\r\n" );
document.write( "\r\n" );
document.write( "N = \"100Q%2F24\"\r\n" );
document.write( "\r\n" );
document.write( "N = \"25Q%2F6\"\r\n" );
document.write( "\r\n" );
document.write( "So we have\r\n" );
document.write( "\r\n" );
document.write( "\"25P%2F47\" = \"25Q%2F6\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 25\r\n" );
document.write( "\r\n" );
document.write( "\"P%2F47\" = \"Q%2F6\"\r\n" );
document.write( "\r\n" );
document.write( "Cross multiply:\r\n" );
document.write( "\r\n" );
document.write( "\"6P\" = \"47Q\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 6Q\r\n" );
document.write( "\r\n" );
document.write( "\"%286P%29%2F%286Q%29\" = \"%2847Q%29%2F%286Q%29\" \r\n" );
document.write( "\r\n" );
document.write( "\"P%2FQ\" = \"47%2F6\"\r\n" );
document.write( "\r\n" );
document.write( "The smallest positive integer values of P and Q\r\n" );
document.write( "which make that equation true are P = 47 and\r\n" );
document.write( "Q = 6.\r\n" );
document.write( "\r\n" );
document.write( "Substitute 47 for P in\r\n" );
document.write( "\r\n" );
document.write( "1.88N = P\r\n" );
document.write( "\r\n" );
document.write( "1.88N = 47\r\n" );
document.write( "\r\n" );
document.write( "N = \"47%2F1.88\"\r\n" );
document.write( "\r\n" );
document.write( "N = 25\r\n" );
document.write( "\r\n" );
document.write( "As a check:\r\n" );
document.write( "\r\n" );
document.write( "Substitute 6 for Q in\r\n" );
document.write( "\r\n" );
document.write( "0.24N = Q\r\n" );
document.write( "\r\n" );
document.write( "0.24N = 6\r\n" );
document.write( "\r\n" );
document.write( "N = \"6%2F0.24\"\r\n" );
document.write( "\r\n" );
document.write( "N = 25\r\n" );
document.write( "\r\n" );
document.write( "So the answer is 25 years. That's the next time when \r\n" );
document.write( "both planets will have each completed a whole number \r\n" );
document.write( "of revolutions.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );