The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9 less than three times the original number. What is the original number? Thank you!

1 Answer
Apr 9, 2017

Answer:

Number is #27#.

Explanation:

Let the unit digit be #x# and tens digit be #y#

then #x+y=9# ........................(1)

and number is #x+10y#

On reversing the digits it will become #10x+y#

As #10x+y# is #9# less than three times #x+10y#, we have

#10x+y=3(x+10y)-9#

or #10x+y=3x+30y-9#

or #7x-29y=-9# ........................(2)

Multiplying (1) by #29# and adding to (2), we get

#36x=9xx29-9=9xx28#

or #x=(9xx28)/36=7#

and hence #y=9-7=2#

and number is #27#.