Question

The sum of the digits of a two-digit number is 6. On reversing the digits, the new number is 18 less than the original number. Find the original number

Answer 1

Let's set up a system with two variables:

x = tens place of our answer,

y = units place of our answer.

Digit sum of a two digit number is 6:

             x+y=6

Reverse the digits and you get 18 less than the original value:

10y + x = 10x + y-18

Now let's solve:

y = 6 - x

10(6-x) + x = 10x + (6-x) - 18

60 - 10x + x = 10x + (6-x) - 18

60 - 9x = 9x - 12

72 = 18x

x = 4

y = 6-4

y=2  

So our original number was 42.