document.write( "Question 504497: I need your help about the applications of System of Linear Equations. This is the problem:\r
\n" ); document.write( "\n" ); document.write( "The sum of the digits of a two digit number is 10. If the digits are reversed, the new number is 18 less than the original number. Find the original number.\r
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\n" ); document.write( "\n" ); document.write( "-thank you.\r
\n" ); document.write( "\n" ); document.write( "I'm having a hard time finding the right equation to use so please help me. :) \n" ); document.write( "
Algebra.Com's Answer #339622 by htmentor(1343)\"\" \"About 
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The sum of the digits of a two digit number is 10. If the digits are reversed, the new number is 18 less than the original number. Find the original number.
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\n" ); document.write( "Let x = the original number
\n" ); document.write( "Let m = the digit representing the tens place
\n" ); document.write( "Let n = the digit representing the ones place
\n" ); document.write( "Since the number x is obtained by multiplying m by 10 and adding n to it, we can write:
\n" ); document.write( "10m + n = x
\n" ); document.write( "If the digits are reversed the number is 18 less, so we have:
\n" ); document.write( "10n + m = x - 18
\n" ); document.write( "The sum of the digits is 10:
\n" ); document.write( "m + n = 10
\n" ); document.write( "So we have 3 equations in 3 unkowns. Solve using your favorite method, substitution, elimination, etc.
\n" ); document.write( "You will get the answers m = 6, n = 4
\n" ); document.write( "So the number is 64
\n" ); document.write( "Check:
\n" ); document.write( "6 + 4 = 10
\n" ); document.write( "64 - 18 = 46 \n" ); document.write( "
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