document.write( "Question 1043164: A certain number of two digits is equal to five times the sum of the digits. Three times the larger digit exceeds three times the smaller by three. Find the number. \n" ); document.write( "

Algebra.Com's Answer #658265 by KMST(5328) $\"\"$ $\"About$

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$\"x\"$ = the larger digit
\n" ); document.write( " $\"y\"$ = the smaller digit
\n" ); document.write( "\"Three times the larger digit exceeds three times the smaller by three\" translates as
\n" ); document.write( " $\"3x=3y%2B3\"$ <--> $\"3%2Ax=3%28y%2B1%29\"$ <--> $\"x=y%2B1\"$ .
\n" ); document.write( "That narrows the possibilities to
\n" ); document.write( "10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, and 98.
\n" ); document.write( "What other clue do we have?\r
\n" ); document.write( "\n" ); document.write( " $\"t\"$ = the tens digit
\n" ); document.write( " $\"u\"$ = the ones digit
\n" ); document.write( " $\"t%2Bu\"$ = the sum of the digits
\n" ); document.write( " $\"10t%2Bu\"$ = the value of the number
\n" ); document.write( "The \"number of two digits is equal to five times the sum of the digits\"
\n" ); document.write( "translates into the equation
\n" ); document.write( " $\"10t%2Bu=5%28t%2Bu%29\"$ <--> $\"10t%2Bu=5t%2B5u\"$ <--> $\"10t-5t=5u-u\"$ <--> $\"5t=4u\"$ <--> $\"t=%284%2F5%29%2Au\"$ .
\n" ); document.write( "Maybe by now you realize that the number is $\"highlight%2845%29\"$ .
\n" ); document.write( "Otherwise, $\"t=%284%2F5%29%2Au\"$ tells you that $\"t\"$ is the smaller digit, so $\"u=t%2B1\"$ .
\n" ); document.write( " $\"system%28u=t%2B1%2C5t=4u%29\"$ ---> $\"system%28u=t%2B1%2C5t=4%28t%2B1%29%29\"$ ---> $\"system%28u=t%2B1%2C5t=4t%2B4%29\"$ ---> $\"system%28u=t%2B1%2C5t-4t=4%29\"$ ---> $\"system%28u=t%2B1%2Ct=4%29\"$ ---> $\"system%28u=4%2B1%2Ct=4%29\"$ ---> $\"highlight%28system%28u=5%2Ct=4%29%29\"$ \n" ); document.write( "

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