document.write( "Question 544540: a two digit number increases by 27 when it is reversed. the unit digit is 1 greater than 3 times the ten digit. Find the number \n" ); document.write( "

Algebra.Com's Answer #355130 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = tens digit
\n" ); document.write( "Let $\"+b+\"$ = units digit
\n" ); document.write( " $\"+10a+%2B+b+\"$ = the value of the number
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+10b+%2B+a+=+10a+%2B+b+%2B+27+\"$
\n" ); document.write( "(2) $\"+b+=+3a+%2B+1+\"$
\n" ); document.write( "------------------
\n" ); document.write( "(1) $\"+-9a+%2B+9b+=+27+\"$
\n" ); document.write( "(1) $\"+-a+%2B+b+=+3+\"$
\n" ); document.write( "(2) $\"+-3a+%2B+b+=+1+\"$
\n" ); document.write( "Subtract (2) from (1)
\n" ); document.write( "(1) $\"+-a+%2B+b+=+3+\"$
\n" ); document.write( "(2) $\"+3a+-+b+=+-1+\"$
\n" ); document.write( " $\"+2a+=+2+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(2) $\"+b+=+3a+%2B+1+\"$
\n" ); document.write( "(2) $\"+b+=+3%2A1+%2B+1+\"$
\n" ); document.write( "(2) $\"+b+=+4+\"$
\n" ); document.write( "The number is 14
\n" ); document.write( "Check answer:
\n" ); document.write( "(1) $\"+10b+%2B+a+=+10a+%2B+b+%2B+27+\"$
\n" ); document.write( "(1) $\"+10%2A4+%2B+1+=+10%2A1+%2B+4+%2B+27+\"$
\n" ); document.write( "(1) $\"+41+=+14+%2B+27+\"$
\n" ); document.write( "(1) $\"+41+=+41+\"$
\n" ); document.write( "OK \n" ); document.write( "

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