The sum of the digits of a certain two-digit number is 7. reversing its digits increases the number by 9.

a + b = 7
10a + b + 9 = 10b + a

9a - 9b = -9
9a = 9b - 9
a = b - 1

Plugging back into the original equation:

(b - 1) + b = 7
2b - 1 = 7
2b = 8
b = 4
a = 3

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