document.write( "Question 1064162: The sum of the digits of a certain two-digits number is 7. When you reverse its digits you increase the number by 27. What is the number. \n" ); document.write( "

Algebra.Com's Answer #679200 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"10a%2Bb\"$ = the number
\n" ); document.write( " $\"10b%2Ba\"$ = the result of reversing the digits
\n" ); document.write( "The clues in the problem translate into two equations:
\n" ); document.write( " $\"a%2Bb=7\"$ = the sum of the digits
\n" ); document.write( " $\"%2810b%2Ba%29-%2810a%2Bb%29=27\"$ = the reversed number minus the original number
\n" ); document.write( "Solving the system:
\n" ); document.write( "Simplifying the second equation we get $\"b=a%2B3\"$ :
\n" ); document.write( " $\"%2810b%2Ba%29-%2810a%2Bb%29=27\"$
\n" ); document.write( " $\"10b%2Ba-10a-b=27\"$
\n" ); document.write( " $\"9b-9a=27\"$
\n" ); document.write( " $\"9%28b-a%29=27\"$
\n" ); document.write( " $\"b-a=27%2F9\"$
\n" ); document.write( " $\"b-a=3\"$
\n" ); document.write( " $\"b=a%2B3\"$
\n" ); document.write( "Substituting $\"a%2B3\"$ for $\"b\"$ in $\"a%2Bb=7\"$
\n" ); document.write( "we get
\n" ); document.write( " $\"a%2Ba%2B3=7\"$
\n" ); document.write( " $\"2a%2B3=7\"$
\n" ); document.write( " $\"2a=7-3\"$
\n" ); document.write( " $\"2a=4\"$
\n" ); document.write( " $\"a=4%2F2\"$
\n" ); document.write( " $\"a=2\"$
\n" ); document.write( "Substituting $\"2\"$ for $\"a\"$ in $\"b=a%2B3\"$ we get
\n" ); document.write( " $\"b=2%2B3\"$
\n" ); document.write( " $\"b=5\"$
\n" ); document.write( "So, the number is $\"highlight%2825%29\"$ \n" ); document.write( "

\n" );