SOLUTION: the sum of the digits of two digit number is 9.if the digits are reversed the new number is decresed by 9.find the number.

Algebra ->  Systems-of-equations -> SOLUTION: the sum of the digits of two digit number is 9.if the digits are reversed the new number is decresed by 9.find the number.      Log On


   

Question 615680: the sum of the digits of two digit number is 9.if the digits are reversed the new number is decresed by 9.find the number.
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the tens digit
and y be the unit digit

So,
10x + y = number
The sum of the digits of a number is 9.
x + y = 9............(1)
Reversing the digits decrease the number by 9.
10y + x = 10x + y - 9
10y - y = 10x - x - 9
9y = 9x - 9
9y = 9(x - 1)
Divide above equation by 9, we have
y = x - 1
y-x=-1..............(2)

Add (1) and (2)
y - x = -1
x + y = 9
--------------
2y=8.........(2)
Divide by 2 both sides
2y/2=8/2
y = 4
Put the value of x in (1)
x+y=9
x+4=9
x=9-4
x=5
Digits are 5 and 4
and number is 54

Check
======
The sum of the digits of a number is 9
5+4=9
9=9
Reversing the digits decrease the number by 9.
45=54-9
45=45