document.write( "Question 623345: what 4 digit number becomes 9x the original number when read backwards \n" ); document.write( "
Algebra.Com's Answer #392070 by ankor@dixie-net.com(22740)\"\" \"About 
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what 4 digit number becomes 9x the original number when read backwards
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\n" ); document.write( "From the information given, we know that 1st digit has to be 1,
\n" ); document.write( "then the last digit had to be 9*1 = 9
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\n" ); document.write( "1st original digit = 1 (thousands)
\n" ); document.write( "let a = 2nd original digit (100's)
\n" ); document.write( "let b = 3rd original digit (10's)
\n" ); document.write( "last original digit = 9 (units)
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\n" ); document.write( "Nine times original number = reversed number
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\n" ); document.write( "9(1000 + 100a + 10b + 9) = 9000 + 100b + 10a + 1
\n" ); document.write( "9000 + 900a + 90b + 81 = 9000 + 100b + 10a + 1
\n" ); document.write( "combine like terms
\n" ); document.write( "900a + 90b + 9081 = 100b + 10a + 9001
\n" ); document.write( "900a - 10a + 90b - 100b + 9081 - 9001 = 0
\n" ); document.write( "890a - 10b + 80 = 0
\n" ); document.write( "simplify, divide by 10
\n" ); document.write( "89a - b + 8 = 0
\n" ); document.write( "b = 89a + 8
\n" ); document.write( "The only value for a that would give a single digit value for b would be 0
\n" ); document.write( "therefore
\n" ); document.write( "a = 0
\n" ); document.write( "b = 8
\n" ); document.write( "Original number 1089
\n" ); document.write( "1089 * 9 = 9801 the reverse \n" ); document.write( "
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