document.write( "Question 409852: The sum of the digits of a two-digit number is 7. The number formed by reversing the digits is two more than double the original number. Find the original number. \n" ); document.write( "

Algebra.Com's Answer #288360 by josmiceli(19441) $\"\"$ $\"About$

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Let the units digit = $\"a\"$
\n" ); document.write( "Let the tens digit = $\"b\"$
\n" ); document.write( "the number is: $\"10b+%2B+a\"$
\n" ); document.write( "the number with reversed digits is: $\"10a+%2B+b\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"a+%2B+b+=+7\"$
\n" ); document.write( "(2) $\"10a+%2B+b+=+2%2A%2810b+%2B+a%29+%2B+2\"$
\n" ); document.write( "---------------------------
\n" ); document.write( "(2) $\"10a+%2B+b+=+20b+%2B+2a+%2B+2\"$
\n" ); document.write( "(2) $\"8a+-+19b+=+2\"$
\n" ); document.write( "Multiply both sides of (1) by $\"8\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"8a+-+19b+=+2\"$
\n" ); document.write( "(1) $\"-8a+-+8b+=+-56\"$
\n" ); document.write( " $\"-27b+=+-54\"$
\n" ); document.write( " $\"b+=+2\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"a+%2B+b+=+7\"$
\n" ); document.write( " $\"a+=+5\"$
\n" ); document.write( "The original number is $\"10b+%2B+a+\"$ = 25
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"10a+%2B+b+=+2%2A%2810b+%2B+a%29+%2B+2\"$
\n" ); document.write( "(2) $\"10%2A5+%2B+2+=+2%2A%2810%2A2+%2B+5%29+%2B+2\"$
\n" ); document.write( "(2) $\"52+=+2%2A25+%2B+2\"$
\n" ); document.write( "(2) $\"52+=+52\"$
\n" ); document.write( "OK \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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