document.write( "Question 778755: The two digits in Jack's age are the same as the digits in Bill's age, but in reverse order. In five years Jack will be twice as old as Bill will be then. What is the difference in their current ages \n" ); document.write( "
Algebra.Com's Answer #474886 by DrBeeee(684)\"\" \"About 
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Let Jack's age = ab,
\n" ); document.write( "Then Bill's age = ba
\n" ); document.write( "In five years we have
\n" ); document.write( "(1) ab + 5 = 2*(ba +5) or
\n" ); document.write( "(2) ab = 2*ba + 5
\n" ); document.write( "Jack's age of ab can be written as
\n" ); document.write( "(3) ab = 10*a + b and Bill's age is
\n" ); document.write( "(4) ba = 10*b + a
\n" ); document.write( "Put (3) and (4) into (2) and get
\n" ); document.write( "(5) 10*a + b = 2*(10*b + a) + 5 or
\n" ); document.write( "(6) 10*a - 2*a = 20*b - b + 5 or
\n" ); document.write( "(7) 8*a = 19*b + 5
\n" ); document.write( "Now we must find integers use (7) a and b that satisfy (7). If we let
\n" ); document.write( "(8) b = {0,1, 2,...,9} and use (7) to find a, we only get the integer pair
\n" ); document.write( "(9) (a,b) = (3,1)
\n" ); document.write( "Let's check this answer with (1).
\n" ); document.write( "Is (31 + 5 = 2*(13 + 5))?
\n" ); document.write( "Is (36 = 2*18))?
\n" ); document.write( "Is (36 = 36)? Yes
\n" ); document.write( "Answwer: The difference between Jack's age and Bill's age is 18.\r
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