SOLUTION: The sum of two digits of a two digit number is 15. If 9 is added to it, the digits are reversed. Find the number.

Question 977923: The sum of two digits of a two digit number is 15. If 9 is added to it, the digits are reversed. Find the number.
Found 3 solutions by richwmiller, Boreal, htmentor:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
a+b=15
10*a+b+9=10*b+a
9a+9=9b
a+1=b
a+a+1=15
2a=14
a=7
b=8
the number is 78
check
78+9=87

Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
let the tens digit =x
let the ones digit= y
The number is 10*x+y;; 10*y+x is the reverse
10x+y+9=10y+x
9x+9=9y. Divide everything in the equation by 9.
x+1=y
Their sum is 15.
x+x+1=15
2x=14
x=7
y=8
The number is 78
Add 9, and you get 87.

Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
This answer can be found without any algebra. Since the number is two digits and the digits add to 15,
the choices are 69, 78, 87, and 96. Adding 9 to 96 gives 105 a 3 digit number. Adding 9 to 87 gives 96, which isn't the reverse of 87.
And 69 + 9 = 78. Again, not the reverse.
So the answer is 78. 78 + 9 = 87
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