The sum of the digits of a two digit positive integer is 15 , when the digits are reversed the number is 27 more than the original number . what was the original number?
+538 Possible numbers
87
78
96
69
The number has to be smaller than its opposite so
78
69
87-78=9
96-69=27
So the number is 69
+128474 Call the digits a and b
So
a + b = 15 ⇒ b = 15 - a
So
Call the original number 10a + (15 - a) and call the resulting number 10(15 - a) + a
So 27 added to the otiginal number = the resulting number
10a + ( 15 - a) + 27 = 10 ( 15 - a) + a
9a + 42 = 150 - 9a
18a = 150 - 42
18a = 108
a= 108 / 18 = 6
And b =15 - 6 = 9
The original number= 69
The resulting number = 69+ 27 = 96
