# The sum of the digits of a two-digit numeral is 8. If the digits are reversed, the new number is 18 greater than the original number. How do you find the original numeral?

Apr 16, 2016

Solve equations in the digits to find the original number was $35$

#### Explanation:

Suppose the original digits are $a$ and $b$. Then we are given:

$\left\{\begin{matrix}a + b = 8 \\ \left(10 b + a\right) - \left(10 a + b\right) = 18\end{matrix}\right.$

The second equation simplifies to:

$9 \left(b - a\right) = 18$

Hence:

$b = a + 2$

Substituting this in the first equation we get:

$a + a + 2 = 8$

Hence $a = 3$, $b = 5$ and the original number was $35$.