SOLUTION: The sum of the digits of 2-digit number is 11.The number obtained by inter changing the digits exceeds the original number by 27.find the number.

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Question 701835: The sum of the digits of 2-digit number is 11.The number obtained by inter changing the digits exceeds the original number by 27.find the number.
Answer by lwsshak3(11628) About Me  (Show Source):
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The sum of the digits of 2-digit number is 11.The number obtained by inter changing the digits exceeds the original number by 27.find the number.
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let u=units digit
let t=tens digit
t+u=11
t=11-u
..
10t+u+27=10u+t
10(11-u)+u+27=10u+11-u
110-10u+u+27=9u+11
127-9u=9u+11
18u=126
u=7
t=11-u
t=4
original number:
=10t+u
=40+7
=47