Mary H. answered • 10/29/15

Tutor for Elem. and Middle Sc. Math, Algebra, Geometry and Sciences

Hi Sabrina,

The sum of the digits is 9. If the tens digit is 'x', and the units digit is 9 - x.

The original number is ten times the tens digit plus the units digit, so the original number is 10x + 9 - x and that can be rearranged to 10x - x + 9, and simplified to 9x + 9.

When the number is reversed, the tens digit will now be ten time 9 - x plus the other digit 'x', which looks like this:

10(9 - x) + x which can be simplified to 90 - 9x + x which becomes 90 - 9x.

The second sentence in your problem says 'Original number minus the second number = 27'

So.... (9x + 9) - (90 - 9x) = 27 which simplifies to 9x + 9 - 90 + 9x = 27 which simplifies to 18x - 81 = 27, add 81 to each side, 18x = 108 and now divide by 18 to get x = 6.

Since x = 6 then 9 - x = 3

So the tens digit is 6 and units digit is 3. The 'number' is 63.

To check, 63 - 36 = 27

Hope this helps, Sabrina,

Mary Ann

Thilak N.

07/14/16