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?

Answer 1

Answer:

53

Step-by-step explanation:

Let's make some equations.

The number is two-digit, so let's make it $xy$

Also, the two digits add up to 8, so $x+y=8$

Now the value of $xy=10x+y$

and the value of $yx=10y+x$

Since we know that when we reverse the digits the number is less than the resulting number by 18, we can formulate an equation.

$10y+x=10x+y+18$

Solve this equation.

$9y-9x=18$

$9(y-x)=18$

$y-x=2$

Now let's use the equation we made earlier.

Change $x+y=8$ into $y=8-x$

Solve the system of equations.

$y-x=2$

$y=8-x$

$8-x-x=2$

$8-2x=2$

$-2x=-6$

$x=3$

$y-3=2$

$y=5$

So the original number is 53.