The sum of the digits of a two digit number is 10. When the digits are reversed, the number increases by 18. Find original number.

Answer 1

10x+y=10y+x-18 multiply the tens digit by 10 and leave the one's digit alone

9x=9y-18 divide by 2

x=y-2

x-y=-2

x+y=10

add above two equations

2x=8 divide by 2

x=4

y=10-4=6

numbers are 46 and 64

64=46+18 4+6=10

alternative method is consider the possible digits that add to 10, that's 5,5, 6,4, 7,3, 8,2 and 9,1

we want digits that when reversed have an 18 difference

55 is the same. 91 and 19 are too far apart, 82 and 28 still too far apart.

73 and 37 are over 30 difference. Only possibility left is 46 and 64. 46 increases by 18 with digits reversed.