# The sum of the digits of a certain two-digit number is 9. Reversing its digits decreases the number by 9. what is the number?

1
by rezter

2015-03-08T04:32:43+08:00

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let x be the tens digit
and y be the unit digit

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.

======
So if you want to be sure if it's right and you want to check it, here it is:
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