document.write( "Question 1085289: A certain number has four digits, the sum of which is 10. If you
\n" ); document.write( "exchange the first and last digits, the new number will be 2997
\n" ); document.write( "larger. If you exchange the middle two digits of the original
\n" ); document.write( "number, your new number will be 90 larger. This enlarged number
\n" ); document.write( "plus the original number equals 2558. What is the original
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Algebra.Com's Answer #699377 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
A certain number has four digits,...
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document.write( "Let A = 1st digit\r\n" );
document.write( "Let B = 2nd digit\r\n" );
document.write( "Let C = 3rd digit\r\n" );
document.write( "Let D = 4th, last, digit\r\n" );
document.write( "So the number = 1000A + 100B + 10C + D \r\n" );
document.write( "

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document.write( "A + B + C + D = 10\r\n" );
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\n" ); document.write( "If you exchange the first and last digits, the new number...
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document.write( "The new number = 1000D + 100B + 10C + A\r\n" );
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document.write( "So\r\n" );
document.write( "1000D + 100B + 10C + A = 1000A + 100B + 10C + D + 2997\r\n" );
document.write( "             1000D + A = 1000A + D + 2997\r\n" );
document.write( "          -999A + 999D = 2997\r\n" );
document.write( "Divide through by 999\r\n" );
document.write( "                -A + D = 3\r\n" );
document.write( "

\n" ); document.write( "If you exchange the middle two digits of the original
\n" ); document.write( "number, your new number will be 90 larger.
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document.write( "The new number = 1000A + 100C + 10B + D\r\n" );
document.write( "

\n" ); document.write( "...will be 90 larger.
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document.write( "So\r\n" );
document.write( "1000A + 100C + 10B + D = 1000A + 100B + 10C + D + 90\r\n" );
document.write( "            100C + 10B = 100B + 10C + 90\r\n" );
document.write( "            -90B + 90C = 90 \r\n" );
document.write( "Divide through by 90\r\n" );
document.write( "                -B + C = 1\r\n" );
document.write( "

\n" ); document.write( "This enlarged number plus the original number equals 2558.
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document.write( "1000A + 100C + 10B + D + 1000A + 100B + 10C + D = 2558\r\n" );
document.write( "                       2000A + 110B + 110C + 2D = 2558\r\n" );
document.write( "Divide through by 2\r\n" );
document.write( "                          1000A + 55B + 55C + D = 1279  \r\n" );
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document.write( "So we have this system of 4 equations in 4 unknowns:\r\n" );
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document.write( "                              A +   B +   C + D =   10   \r\n" );
document.write( "                             -A             + D =    3\r\n" );
document.write( "                                   -B +   C     =    1 \r\n" );
document.write( "                          1000A + 55B + 55C + D = 1279\r\n" );
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document.write( "Solve this system by either substitution, elimination,\r\n" );
document.write( "or matrices or a combination of those, we get\r\n" );
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document.write( "                             A = 1, B = 2, C = 3, D = 4\r\n" );
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document.write( "So the desired number is 1234.\r\n" );
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document.write( "Edwin
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