The sum of the digits of a two- digit number is 9. If the digits are reversed, the new number is 9 larger than the original number. What is the original number?

Answer 1

o = ones digit

t = tens digit

sum of tens and ones digit is 9:

o + t = 9

t = 9 - o

number formed by reversing tens and ones digit is 10*o + t

number formed by original tens and ones digits is 10*t + o, then add 9:

10*o + t = o + 10*t + 9

substitute 9-o for t:

10*o + 9 - o = o + 10*(9-o) + 9

solve for o:

9o + 9 = o + 90 - 10o + 9

9o + 9 = -9o + 99

18o = 90

o = 5

solve for t:

t = 4

original number is 45