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#.