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

C

Explanation:

Answer 2

53

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.