Answer:
The three-digit numbers with these properties are 850 or 941.
Step-by-step explanation:
Let x be the hundreds digit, y the tens digit, and z the ones digit. The first condition says that [tex]y+z=5[/tex]. The second condition is:
the original number is [tex](100x+10y+z)[/tex] while the reversed number is [tex](100z+10y+x)[/tex] so
[tex](100x+10y+z)-(100z+10y+x)=792\\99x-99z=792[/tex]
Now we have the system
[tex]y+z=5\\ 99x-99z=792[/tex]
You can divide by 99 to simplify the second equation.
[tex]y+z=5\\ x-z=8[/tex]
Note that x, y, z must be digits between 0 and 9 and [tex]x\neq 0[/tex]. If [tex]z>1[/tex], then the second equation forces [tex]x>9[/tex], for example z=2 so x-2=8, x=10 which is impossible. If z=0, you get x=8, y=5 and the number is 850. If z=1, you get x=9,y=4 and the number is 941.
