Answer:
53
Step-by-step explanation:
Let's make some equations.
The number is two-digit, so let's make it [tex]xy[/tex]
Also, the two digits add up to 8, so [tex]x+y=8[/tex]
Now the value of [tex]xy=10x+y[/tex]
and the value of [tex]yx=10y+x[/tex]
Since we know that when we reverse the digits the number is less than the resulting number by 18, we can formulate an equation.
[tex]10y+x=10x+y+18[/tex]
Solve this equation.
[tex]9y-9x=18[/tex]
[tex]9(y-x)=18[/tex]
[tex]y-x=2[/tex]
Now let's use the equation we made earlier.
Change [tex]x+y=8[/tex] into [tex]y=8-x[/tex]
Solve the system of equations.
[tex]y-x=2[/tex]
[tex]y=8-x[/tex]
[tex]8-x-x=2[/tex]
[tex]8-2x=2[/tex]
[tex]-2x=-6[/tex]
[tex]x=3[/tex]
[tex]y-3=2[/tex]
[tex]y=5[/tex]
So the original number is 53.
