SOLUTION: The sum of the digits of a two-digit number is 13. If the digits are reversed, the original number is 45 less than the new number. Find the original number.

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Question 950226: The sum of the digits of a two-digit number is 13. If the digits are reversed, the original number is 45 less than the new number. Find the original number.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
T=tens digit; N=ones digit
T+N=13
T=13-N
10T+N=(10N+T)-45 Substitute for T
10(13-N)+N=10N+(13-N)-45
130-9N=9N-32 Add (9N+32) to each side.
162=18N divide each side by 18.
9=N ANSWER 1: The original units digit was 9
T=13-n=13-9=4 ANSWER 2:The original tens digit was 4
ANSWER The two digit number is 49
CHECK:
49=94-45
49=49