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?

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Answer 1 · 2016-04-16T23:50:24

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

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

${ (a+b=8), ((10b+a)-(10a+b) = 18) :}$

The second equation simplifies to:

$9(b-a) = 18$

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 $35$ .