document.write( "Question 943508: How many 3- digit even numbers are there that have 24 as the sum of their digits?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #575207 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
THE SECOND GRADER ANSWER (we do not even need a fifth grader here):
\n" ); document.write( "If the sum is 24, no digit can be zero,
\n" ); document.write( "because the sum of the other two digits can be at most 9+9=18<24.
\n" ); document.write( "In fact, no digit could even be less than 5,
\n" ); document.write( "because that would make the sum less than 5+9+9=23.
\n" ); document.write( "If the number is even, the last digit must be even,
\n" ); document.write( "and adding the requirement of being more than 5,
\n" ); document.write( "it has to be 6 or 8.
\n" ); document.write( "
\n" ); document.write( "IF the last digit is 6,
\n" ); document.write( "the other two digits must be 9,
\n" ); document.write( "because 6+x+y=24 means that x+y=24-6, which means x+y=18.
\n" ); document.write( "So the only choice is $\"red%28996%29\"$ .
\n" ); document.write( "
\n" ); document.write( "IF the last digit is 8,
\n" ); document.write( "the other two digits must add up to 24-8=16.
\n" ); document.write( "The choices are
\n" ); document.write( "8+8=16, which would give us the number $\"red%28886%29\"$ , and
\n" ); document.write( "7+9=16, which gives us $\"red%28798%29\"$ and $\"red%28978%29\"$ .
\n" ); document.write( "
\n" ); document.write( "How many number could we make?
\n" ); document.write( "Let me count them.
\n" ); document.write( "We made $\"highlight%28red%284%29%29\"$ numbers that
\n" ); document.write( "had 3 digits,
\n" ); document.write( "were even, and
\n" ); document.write( "their digits added to 24. \n" ); document.write( "

\n" );