The sum of the digits of a certain two digit number is 14. When you reverse its digits you decrease the number by 18. What is the number?

systems of elimination word problems

1 Answer
Feb 21, 2018

Let the number be

#10x+y#
where #y# is digit in Units place and #x# is the digit in Tens place.

Given

  1. #x+y=14# .......(1)
  2. Number with digits reversed is #18# more than original number
    #:.10y+x=10x+y+18#
    #=>9x-9y=-18#
    #=>x-y=-2# ......(2)

Adding (1) and (2) we get

#2x=12#
#x=12/2=6#

Using (1)

#y=14-6=8#

Number is

#10xx 6+8=68#