document.write( "Question 891658: the sum of the digits of a three digit number is 19. The hundreds digit is three times the tens digit. The number is 198 more than the number reversed. Find the original number. \n" ); document.write( "

Algebra.Com's Answer #539932 by Fombitz(32388) $\"\"$ $\"About$

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$\"H\"$ - hundreds place digit
\n" ); document.write( " $\"T\"$ - tens place digit
\n" ); document.write( " $\"U\"$ - ones place digit
\n" ); document.write( "1. $\"H%2BT%2BU=19\"$
\n" ); document.write( "2. $\"H=3T\"$
\n" ); document.write( " $\"H%2A100%2BT%2A10%2BU=198%2BU%2A100%2BT%2A10%2BH\"$
\n" ); document.write( " $\"100H%2BU=100U%2B198%2BH\"$
\n" ); document.write( " $\"99H-99U=198\"$
\n" ); document.write( "3. $\"H-U=2\"$
\n" ); document.write( "Substituting eq. 2 into eq. 1 and eq. 3,
\n" ); document.write( " $\"3T%2BT%2BU=19\"$
\n" ); document.write( "4. $\"4T%2BU=19\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "5. $\"3T-U=2\"$
\n" ); document.write( "Add eqs.4 and 5,
\n" ); document.write( " $\"4T%2BU%2B3T-U=19%2B2\"$
\n" ); document.write( " $\"7T=21\"$
\n" ); document.write( " $\"T=3\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"4%283%29%2BU=19\"$
\n" ); document.write( " $\"U=19-12\"$
\n" ); document.write( " $\"U=7\"$
\n" ); document.write( "And,
\n" ); document.write( " $\"H=3T\"$
\n" ); document.write( " $\"H=3%283%29\"$
\n" ); document.write( " $\"H=9\"$
\n" ); document.write( "The original number is 937.
\n" ); document.write( " \n" ); document.write( "

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