Question 175629
If the digits of a two-digit positive integer are reversed, the result is 6 less than twice the original number. Find all such integers for which this is true.
:
Let x = the 10's digit
Let y = the units digit
then
10x + y = original integer
and
10y + x = reversed digit number
:
Write an equation for what it says:
10y + x = 2(10x + y) - 6
:
10y + x = 20x + 2y - 6
:
10y - 2y = 20x - x - 6
:
8y = 19x - 6
y = {{{(19x-6)/8}}}
You can see there are not many values for x which will result in a single digit integer for y.
:
x=1 obviously not (13/8)
x=2
y = {{{(19*2)-6)/8}}}
y = {{{(38-6)/8}}}
y = 32/8
y = 4
Our original number = 24, and you will find that this is the only one.