SOLUTION: The sum of digits of a two-digit number is 9. On interchanging the order of the digits,the number becomes 27 more then the original number.find the number

Question 1063056: The sum of digits of a two-digit number is 9. On interchanging the order of the digits,the number becomes 27 more then the original number.find the number
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
The sum of digits of a two-digit number is 9. On interchanging the order of the digits,the number becomes 27 more then the original number.find the number
Let a be the 10's digit
and b be the 1's digit
The number is 10a+b
(1) a+b = 9 (given)
(2) 10b+a = (10a+b)+27 (interchanging digits results in a number that is 27 greater than original)
(1) ==> a=9-b
Substitute for '9-b' for 'a' in (2), that will give us an equation with just 'b' and we can solve for 'b'
10b + (9-b) = (10(9-b) + b) + 27
9b + 9 = 90 - 10b + b + 27
9b + 9 = 117 - 9b
18b = 108
b = 108/18 = 6
b=6 ==> a=9-6=3 (from (1))
The number is
--
Check:
3+6 = 9 (ok)
36 + 27 = 63 (= the interchanged version of 36, ok)

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