document.write( "Question 174725: the sum of the digits of a two-digit number is 10. If the digits are reversed, the number is increased by 72. What is the original number? \n" ); document.write( "

Algebra.Com's Answer #129782 by josmiceli(19441) $\"\"$ $\"About$

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Call the units digit $\"n\"$
\n" ); document.write( "Call the tens digit $\"m\"$
\n" ); document.write( "Given:
\n" ); document.write( " $\"n+%2B+m+=+10\"$
\n" ); document.write( "The actual value of the number is
\n" ); document.write( " $\"10m+%2B+n\"$
\n" ); document.write( "The value of the number with the digits reversed is
\n" ); document.write( " $\"10n+%2B+m\"$
\n" ); document.write( "Given:
\n" ); document.write( " $\"10n+%2B+m+=+10m+%2B+n+%2B+72\"$
\n" ); document.write( "(1) $\"9n+-+9m+=+72\"$
\n" ); document.write( "(2) $\"n+%2B+m+=+10\"$
\n" ); document.write( "Multiply both sides of (2) by $\"9\"$ and add to (1)
\n" ); document.write( "(1) $\"9n+-+9m+=+72\"$
\n" ); document.write( "(2) $\"9n+%2B+9m+=+90\"$
\n" ); document.write( "(3) $\"18n+=+162\"$
\n" ); document.write( " $\"n+=+9\"$
\n" ); document.write( " $\"n+%2B+m+=+10\"$
\n" ); document.write( " $\"m+=+10+-+9\"$
\n" ); document.write( " $\"m+=+1\"$
\n" ); document.write( "The original number is 19
\n" ); document.write( "check:
\n" ); document.write( " $\"91+=+19+%2B+72\"$
\n" ); document.write( " $\"91+=+91\"$
\n" ); document.write( "OK \n" ); document.write( "

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