document.write( "Question 140813: the sum of a two digit number is 10. if 18 be subtracted from it, the digits in the resulting number will be equal. the number is??? \n" ); document.write( "

Algebra.Com's Answer #102521 by solver91311(24713) $\"\"$ $\"About$

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Did you mean that the 'sum of the digits of a two digit number is 10'? I hope so, otherwise what you said makes no sense at all.\r
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\n" ); document.write( "\n" ); document.write( "x is the tens digit
\n" ); document.write( "y is the ones digit\r
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\n" ); document.write( "\n" ); document.write( "x + y = 10\r
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\n" ); document.write( "\n" ); document.write( "The number itself is 10x + y\r
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\n" ); document.write( "\n" ); document.write( "Subtract 18: 10x + y - 18\r
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\n" ); document.write( "\n" ); document.write( "If the digits are the same after subtracting 18, then x - 1 = y - 8 => x - y = -7 (if y >=8) or x - 2 = y + (10 - 8) => x - y = 4 (if y < 8)\r
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\n" ); document.write( "\n" ); document.write( "so, if y >= 8
\n" ); document.write( "x - y = -7
\n" ); document.write( "x + y = 10\r
\n" ); document.write( "\n" ); document.write( "2x = 3 => x not an integer, and y must be less than 8\r
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\n" ); document.write( "\n" ); document.write( "so
\n" ); document.write( "x - y = 4
\n" ); document.write( "x + y = 10\r
\n" ); document.write( "\n" ); document.write( "2x = 14
\n" ); document.write( "x = 7
\n" ); document.write( "y = 3\r
\n" ); document.write( "\n" ); document.write( "The number is 73.\r
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\n" ); document.write( "\n" ); document.write( "Check
\n" ); document.write( "7 + 3 = 10
\n" ); document.write( "73 - 18 = 55
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