Question

The sum of the digits of a two-digit counting number is 13. When the digits are reversed, the new number is 45 greater than the original number. What was the original number? Please show work.

Answer 1

x + y = 13
10x + y = 10y + x + 45

x = 13-y
so 10(13-y) + y = 10y + 13 -y + 45
130 - 13 - 45 = 10y -y - y
72 = 8y
y = 9
so x = 13-9 = 4

the original number was 49