document.write( "Question 390239: A two digit number is 4 times the sum of its digits. If 27 is added to that number its digits are reversed. Find that number. \n" ); document.write( "

Algebra.Com's Answer #276655 by josmiceli(19441) $\"\"$ $\"About$

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Let the 2 digit number = $\"10a+%2B+b\"$
\n" ); document.write( "where $\"a\"$ and $\"b\"$ are the digits
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"10a+%2B+b+=+4%2A%28a+%2B+b%29\"$
\n" ); document.write( "(2) $\"10a+%2B+b+%2B+27+=+10b+%2B+a\"$
\n" ); document.write( "Note that the number with the digits reversed is $\"10b+%2B+a\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "From (1):
\n" ); document.write( " $\"10a+%2B+b+=+4a+%2B+4b\"$
\n" ); document.write( " $\"6a+=+3b\"$
\n" ); document.write( " $\"2a+=+b\"$
\n" ); document.write( "From (2):
\n" ); document.write( " $\"10a+%2B+b+%2B+27+=+10b+%2B+a\"$
\n" ); document.write( "Using substitution:
\n" ); document.write( " $\"10a+%2B+2a+%2B+27+=+10%2A2a+%2B+a\"$
\n" ); document.write( " $\"12a+%2B+27+=+20a++%2B+a\"$
\n" ); document.write( " $\"9a+=+27\"$
\n" ); document.write( " $\"a+=+3\"$
\n" ); document.write( "and
\n" ); document.write( " $\"b+=+2a\"$
\n" ); document.write( " $\"b+=+6\"$
\n" ); document.write( "The number is 36
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"10a+%2B+b+=+4%2A%28a+%2B+b%29\"$
\n" ); document.write( " $\"10%2A3+%2B+6+=+4%2A%283+%2B+6%29\"$
\n" ); document.write( " $\"36+=+4%2A9\"$
\n" ); document.write( " $\"36+=+36\"$
\n" ); document.write( "OK
\n" ); document.write( "(2) $\"10a+%2B+b+%2B+27+=+10b+%2B+a\"$
\n" ); document.write( " $\"10%2A3+%2B+6+%2B+27+=+10%2A6+%2B+3\"$
\n" ); document.write( " $\"63+=+60+%2B+3\"$
\n" ); document.write( " $\"63+=+63\"$
\n" ); document.write( "OK \n" ); document.write( "

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