document.write( "Question 150606This question is from textbook
\n" ); document.write( ": The units digit of a two-digit number is 3 less than its tens digit. If the number is divided by the sum of its digits, the quotient is 6 and the remainder is 8. Find the number. \n" ); document.write( "

Algebra.Com's Answer #110546 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"u\"$ = the units digit
\n" ); document.write( "Let $\"t\"$ = the tens digit
\n" ); document.write( " $\"u+=+t+-+3\"$
\n" ); document.write( " $\"t+-+u+=+3\"$
\n" ); document.write( "The sum of the digits is $\"t+%2B+u\"$
\n" ); document.write( "The actual number is $\"10t+%2B+u\"$
\n" ); document.write( " $\"%2810t+%2B+u%29+%2F+%28t+%2B+u%29+=+6+%2B+8+%2F+%28t+%2B+u%29\"$
\n" ); document.write( "If the way I wrote the remainder bothers you, think about
\n" ); document.write( " $\"19+%2F+11+=+1+%2B+%288%2F11%29\"$ It's really the same thing
\n" ); document.write( "continuing,
\n" ); document.write( "Multiply each side by $\"t+%2B+u\"$
\n" ); document.write( " $\"10t+%2B+u+=+6%2A%28t+%2B+u%29+%2B+8\"$
\n" ); document.write( " $\"10t+%2B+u+=+6t+%2B+6u+%2B+8\"$
\n" ); document.write( "(1) $\"4t+-+5u+=+8\"$
\n" ); document.write( "And, from above,
\n" ); document.write( " $\"t+-+u+=+3\"$
\n" ); document.write( "Multiply times $\"4\"$
\n" ); document.write( "(2) $\"4t+-+4u+=+12\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( " $\"u+=+4\"$
\n" ); document.write( " $\"t+-+u+=+3\"$
\n" ); document.write( " $\"t+-+4+=+3\"$
\n" ); document.write( " $\"t+=+7\"$
\n" ); document.write( "The number is 74
\n" ); document.write( "check:
\n" ); document.write( "The units digit is 3 less than the tens digit OK
\n" ); document.write( "The number divided by the sum of it's digts is
\n" ); document.write( " $\"74+%2F+11+=+6+%2B+%288%2F11%29\"$ OK \n" ); document.write( "

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