document.write( "Question 795673: The value of a certain two-digit number is eight times the sum of its digits. If the digits of the number are reversed, the result is 45 less than the original number. Find the original number.\r
\n" ); document.write( "\n" ); document.write( "What I tried:
\n" ); document.write( "x- one's digit t- ten's digit
\n" ); document.write( "t=8(x+t)
\n" ); document.write( "t-45= 1/8 x \n" ); document.write( "

Algebra.Com's Answer #481103 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = the tens digit
\n" ); document.write( "Let $\"+u+\"$ = the units digit
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\n" ); document.write( "The actual value of the number is:
\n" ); document.write( " $\"+10t+%2B+u+\"$
\n" ); document.write( "-----------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+10t+%2B+u+=+8%2A%28+t+%2B+u+%29+\"$
\n" ); document.write( "(2) $\"+10u+%2B+t+=+10t+%2B+u+-+45+\"$ ( this is reversing the digits )
\n" ); document.write( "---------------------------
\n" ); document.write( "(1) $\"+10t+%2B+u+=+8t+%2B+8u+\"$
\n" ); document.write( "(1) $\"+2t+=+7u+\"$
\n" ); document.write( "(1) $\"+t+=+%287%2F2%29%2Au+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+10u+%2B+t+=+10t+%2B+u+-+45+\"$
\n" ); document.write( "(2) $\"+9t+-+9u+=+45+\"$
\n" ); document.write( "(2) $\"+t+-+u+=+5+\"$
\n" ); document.write( "Plug (1) into (2)
\n" ); document.write( "(2) $\"+%287%2F2%29%2Au+-+u+=+5+\"$
\n" ); document.write( "(2) $\"+%285%2F2%29%2Au+=+5+\"$
\n" ); document.write( "(2) $\"+u%2F2+=+1+\"$
\n" ); document.write( "(2) $\"+u+=+2+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+t+=+%287%2F2%29%2A2+\"$
\n" ); document.write( "(1) $\"+t+=+7+\"$
\n" ); document.write( "The original number was 72
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+10t+%2B+u+=+8%2A%28+t+%2B+u+%29+\"$
\n" ); document.write( "(1) $\"+10%2A7+%2B+2+=+8%2A%28+7+%2B+2+%29+\"$
\n" ); document.write( "(1) $\"+72+=+8%2A9+\"$
\n" ); document.write( "(1) $\"+72+=+72+\"$
\n" ); document.write( "OK
\n" ); document.write( "(2) $\"+10u+%2B+t+=+10t+%2B+u+-+45+\"$
\n" ); document.write( "(2) $\"+10%2A2+%2B+7+=+10%2A7+%2B+2+-+45+\"$
\n" ); document.write( "(2) $\"+27+=+70+%2B+2+-+45+\"$
\n" ); document.write( "(2) $\"+27+=+27+\"$
\n" ); document.write( "OK\r
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