document.write( "Question 1159944: A two digit number is such that its value equals four times the sum of its digits.If 27 is added to the number the results is equal to the value of the number obtained when the digits are interchanged.What is the number? \n" ); document.write( "

Algebra.Com's Answer #783073 by math_helper(2461) $\"\"$ $\"About$

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document.write( "N = the two-digit number = 10a + b    (1)\r
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document.write( "We are told  
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document.write( " 4a+4b = N             (2)
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document.write( "  and  
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document.write( " 10a+b + 27 = 10b + a  (3)  (27 added to the number results in reversal of digits)\r
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document.write( "(1) and (2) can be used to eliminate N:
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document.write( "   10a+b = 4a+4b\r
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document.write( "This simplfies to  6a-3b = 0
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document.write( "(3) simplifies to  9a-9b = -27\r
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document.write( "These last two equations can be solved easily for  a=3, b=6  ==> \r
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document.write( "Check:
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document.write( "3(4)+6(4) = 12+24 = 36  (ok)
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document.write( "36 + 27 = 63    (digits reversed, ok)\r
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