Question
when you reverse the digits of the number 13,the number increases by 18.how many other 2digit numbers increase by 18 when their digits are reversed ?
Answers
Reiny
let the unit digit be x and the tens digit be y
then the number is 10y + x
and the number reversed would be 10x + y
but 10x + y - (10y + x) = 18
9x - 9y = 18
x-y = 2
this works for:
3,1 ---> our given case
4,2
5,3
6,4
7,5
8,6
and 9,7
check 7,5
if x=7, y = 5
the original number was 57
number reversed 75
and 75 - 57 = 18
then the number is 10y + x
and the number reversed would be 10x + y
but 10x + y - (10y + x) = 18
9x - 9y = 18
x-y = 2
this works for:
3,1 ---> our given case
4,2
5,3
6,4
7,5
8,6
and 9,7
check 7,5
if x=7, y = 5
the original number was 57
number reversed 75
and 75 - 57 = 18