document.write( "Question 1011610: A 6-digit number begins with a 1. However, if the 1 is put at the end of the number instead of at the start,
\n" ); document.write( "the resulting 6-digit number is 3 times the original number. Find the number. \n" ); document.write( "

Algebra.Com's Answer #627335 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A 6-digit number begins with a 1. However, if the 1 is put at the end of the number instead of at the start,
\n" ); document.write( "the resulting 6-digit number is 3 times the original number. Find the number.
\n" ); document.write( "-------------------------------------------------------------------\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "We can write the given 6-digit number starting with 1 as\r\n" );
document.write( "\r\n" );
document.write( "n = 100000 + a,\r\n" );
document.write( "\r\n" );
document.write( "where 100000 is the number produced by the \"1\" in the most left position, \r\n" );
document.write( "and \"a\" is the number written by the digits in positions from 2 to 6.\r\n" );
document.write( "\r\n" );
document.write( "When the \"1\" is put at the end, we get the number\r\n" );
document.write( "\r\n" );
document.write( "m = 10a + 1.\r\n" );
document.write( "\r\n" );
document.write( "Now, the condition says that 3n = m. It gives you an equation for a:\r\n" );
document.write( "\r\n" );
document.write( "3*(100000 + a) = 10a + 1.\r\n" );
document.write( "\r\n" );
document.write( "Simplify and solve it:\r\n" );
document.write( "\r\n" );
document.write( "30000 + 3a = 10a +1,\r\n" );
document.write( "\r\n" );
document.write( "7a = 299999,\r\n" );
document.write( "\r\n" );
document.write( "a =  = 42857.\r\n" );
document.write( "\r\n" );
document.write( "So, the original number was 142857.\r\n" );
document.write( "

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

\n" );