document.write( "Question 669621: Twice the tens digit of a two digit number increased by the units digit is 19. If the digits are reversed, the new number is 45 less than the original number . Find the original number \n" ); document.write( "
Algebra.Com's Answer #416491 by DrBeeee(684)\"\" \"About 
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Let t = ten's digit
\n" ); document.write( "Let u = unit's digit
\n" ); document.write( "Then your original number, n, is
\n" ); document.write( "(1) n = 10*t + u
\n" ); document.write( "You are given that
\n" ); document.write( "(2) 2*t + u = 19 and
\n" ); document.write( "when you interchange t and u, the new number is 45 less than n, or
\n" ); document.write( "(3) 10*u + t = n -45 or
\n" ); document.write( "(4) 10*u + t = 10*t + u -45 or
\n" ); document.write( "(5) 9*u - 9*t = -45 or
\n" ); document.write( "(6) 9*t - 9*u = 45
\n" ); document.write( "Substituting (2) into (6) we get
\n" ); document.write( "(7) 9*t - 9*(19 - 2*t) = 45 or
\n" ); document.write( "(8) 9*t - 171 + 18*t = 45 or
\n" ); document.write( "(9) 27*t = 216 or
\n" ); document.write( "(10) t = 8
\n" ); document.write( "Using (2) we get
\n" ); document.write( "(11) 2*8 + u = 19 or
\n" ); document.write( "(12) u = 3
\n" ); document.write( "Always check your answer. Use (4).
\n" ); document.write( "Is (10*3 + 8 = 10*8 + 3 -45)?
\n" ); document.write( "Is (38 = 83 - 45)?
\n" ); document.write( "Is (38 = 38)? Yes
\n" ); document.write( "Answer: The original number is 83.
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