The sum of the in a two digit number is 17. lf the digits are reversed, the new digits number will be 9 less than the original number. What is the original number?

1 Answer
Oct 4, 2016

The number is #98#

Explanation:

Let the number be #10x+y#

So we can write

#x+y=17#------------------------------Eq #1#

Reverse of the number will be #10y+x#

So we can write

#(10x+y)-(10y+x)=9#

or

#9x-9y=9#

or

#9(x-y)=9#

or

#x-y=9/9#

or

#x-y=1#-------------------Eq #2#

Adding up the Eq #1# and Eq #2#

we get

#x+y+x-y=17+1#

or

#2x+0=18#

or

#2x=18#

or

#x=18/2#

or

#x=9#

By plugging the value #x=9# in the #x+y=17#

We get

#9+y=17#

or

#y=17-9#

or

#y=8#

Therefore the number is #98#