document.write( "Question 724360: Need help with set up please!! I know the answer is 83 through playing with numbers, but I need to show it algebraically. thanks in advance\r
\n" ); document.write( "\n" ); document.write( "The tens digit of a two-digit number is 5 more than the units digit. If \"the number\" is divided by the sum of its digits, the partial quotient is 7 and the remainder is 6. Find \"the number.\" \n" ); document.write( "
Algebra.Com's Answer #443716 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let \"+u+\" = the units digit
\n" ); document.write( "Let \"+t+\" = the tens digit
\n" ); document.write( "given:
\n" ); document.write( "(1) \"+t+=+u+%2B+5+\"
\n" ); document.write( "(2) \"+%28+10t+%2B+u+%29+%2F+%28+t+%2B+u+%29+=+7+%2B+6%2F%28+t+%2B+u+%29+\"
\n" ); document.write( "------------------
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2)
\n" ); document.write( "(2) \"+%28+10u+%2B+50+%2B+u+%29+%2F+%28+2u+%2B+5+%29+=+7+%2B+6%2F%28+2u+%2B+5+%29+\"
\n" ); document.write( "Multiply both sides by \"+2u+%2B+5+\"
\n" ); document.write( "(2) \"+11u+%2B+50+=+7%2A%28+2u+%2B+5+%29+%2B+6+\"
\n" ); document.write( "(2) \"+11u+%2B+50+=+14u+%2B+35+%2B+6+\"
\n" ); document.write( "(2) \"+3u+=+9+\"
\n" ); document.write( "(2) \"+u+=+3+\"
\n" ); document.write( "and, since
\n" ); document.write( "(1) \"+t+=+u+%2B+5+\"
\n" ); document.write( "(1) \"+t+=+3+%2B+5+\"
\n" ); document.write( "(1) \"+t+=+8+\"
\n" ); document.write( "The number is 83
\n" ); document.write( "check answer:
\n" ); document.write( "(2) \"+%28+10t+%2B+u+%29+%2F+%28+t+%2B+u+%29+=+7+%2B+6%2F%28+t+%2B+u+%29+\"
\n" ); document.write( "(2) \"+%28+10%2A8+%2B+3+%29+%2F+%28+8+%2B+3+%29+=+7+%2B+6%2F%28+8+%2B+3+%29+\"
\n" ); document.write( "(2) \"+83%2F11+=+7+%2B+6%2F11+\"
\n" ); document.write( "(2) \"+83+=+77+%2B+6+\"
\n" ); document.write( "(2) \"+83+=+83+\"
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "
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