document.write( "Question 551147: The sum of the digits of a certain two digit number is eight. If the original number is subtracted from the number formed by interchanging the digits, the result is -18. What is the original number? Please help!!! \n" ); document.write( "

Algebra.Com's Answer #359440 by josmiceli(19441) $\"\"$ $\"About$

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Let the 10's digit = $\"a\"$
\n" ); document.write( "Let the 1's digit = $\"+b+\"$
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+8+\"$
\n" ); document.write( "(2) $\"+%28+10b+%2B+a+%29+-+%28+10a+%2B+b+%29+=+-18+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( "(2) $\"+10b+%2B+a+-+10a+-+b+=+-18+\"$
\n" ); document.write( "(2) $\"+-9a+%2B+9b+=+-18+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"9\"$
\n" ); document.write( "and add (1) and (2)
\n" ); document.write( "(1) $\"+9a+%2B+9b+=+72+\"$
\n" ); document.write( "(2) $\"+-9a+%2B+9b+=+-18+\"$
\n" ); document.write( " $\"+18b+=+54+\"$
\n" ); document.write( " $\"+b+=+3+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+8+\"$
\n" ); document.write( "(1) $\"+a+%2B+3+=+8+\"$
\n" ); document.write( "(1) $\"+a+=+5+\"$
\n" ); document.write( "The original number is 53
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28+10%2A3+%2B+5+%29+-+%28+10%2A5+%2B+3+%29+=+-18+\"$
\n" ); document.write( "(2) $\"+30+%2B+5+-+50+-+3+=+-18+\"$
\n" ); document.write( "(2) $\"+35+-+53+-+-18+\"$
\n" ); document.write( "(2) $\"+-18+=+-18+\"$
\n" ); document.write( "OK \n" ); document.write( "

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