SOLUTION: 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 nu

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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
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = ten's digit
Let u = unit's digit
Then your original number, n, is
(1) n = 10*t + u
You are given that
(2) 2*t + u = 19 and
when you interchange t and u, the new number is 45 less than n, or
(3) 10*u + t = n -45 or
(4) 10*u + t = 10*t + u -45 or
(5) 9*u - 9*t = -45 or
(6) 9*t - 9*u = 45
Substituting (2) into (6) we get
(7) 9*t - 9*(19 - 2*t) = 45 or
(8) 9*t - 171 + 18*t = 45 or
(9) 27*t = 216 or
(10) t = 8
Using (2) we get
(11) 2*8 + u = 19 or
(12) u = 3
Always check your answer. Use (4).
Is (10*3 + 8 = 10*8 + 3 -45)?
Is (38 = 83 - 45)?
Is (38 = 38)? Yes
Answer: The original number is 83.