Question

The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?

Answers

Ms. Sue
53
Henry
Sum = 8 = 7+1 = 6+2 = 5+3 = 4+4
Select 5, and 3:
Original #: 53.
Reversed: 35.
Difference = 53-35 = 18.

DrBob222
Here is how you do this with algebra.
Let x = 10s digit
and y = units digit.
So the number is 10x + y
and you know that if you reverse the number it is 10y + x.
The problem tells you that
10x + y = 10y+x+18 which simplifies to
9x-9y=18
The second equation is x + y = 8. Solve those two equations simultaneously this way.
9x-9y = 18
x+y=8
---------
Multiply equation 2 by 9 and you have these two equations.
9x - 9y = 18
9x + 9y = 72
-------------
add
18x = 90
x = 90/18 = 5 which is the 10s digit.

Since x + y = 8, then
5 + y = 8 and y = 8-5=3 which is the units digit so the number is 53

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