Question

A three-digit number has two properties. The tens-digit and the ones-digit add up to 5. If the number is written with the digits in the reverse order, and then subtracted from the original number, the result is 792. Use a system of equations to nd all of the three-digit numbers with these properties

Answer 1

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 $y+z=5$. The second condition is:

the original number is $(100x+10y+z)$ while the reversed number is $(100z+10y+x)$ so

$(100x+10y+z)-(100z+10y+x)=792\\99x-99z=792$

Now we have the system

$y+z=5\\ 99x-99z=792$

You can divide by 99 to simplify the second equation.

$y+z=5\\ x-z=8$

Note that x, y, z must be digits between 0 and 9 and $x\neq 0$. If $z>1$, then the second equation forces $x>9$, 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.