document.write( "Question 1194496: A number with two digits is equal to four times the sum of its digits. The number formed by reversing the order of the digit is 27 greater than the given number. Find the number
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Algebra.Com's Answer #826697 by math_helper(2461) $\"\"$ $\"About$

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document.write( "A number of two digits, written \"ab\" has value  10a + b\r
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document.write( "4(a+b) = 10a + b              (eq 1)\r
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document.write( "Reversing the digits means writing it as \"ba\" which has value 10b + a:\r
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document.write( "10b + a = (10a + b) + 27      (eq 2)\r
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document.write( "Simplify both equations:
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document.write( "(eq 1) simplifies to  2a - b = 0  ---> b = 2a
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document.write( "(eq 2) simplifies to   b - a = 3  
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document.write( "Using substitution (b = 2a) into the simplified (eq 2)  gives
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document.write( "      2a - a = 3     or    a = 3   --->  b = 6
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document.write( "The number is \r
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document.write( "Check:
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document.write( "4(3+6) = 4*9 = 36  (ok on first condition)
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document.write( "63 = 27 + 36    (ok on 2nd condition)
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