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

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So let's call the two-digit number AB where each of A and B is a digit.  This is the same as 10A + B.  Also, A+B=7Reversing the number gets us BA or 10B + A.So 10B + A = 9 + 10A + B.  We'll substitute B = 7 - A.10 (7 - A) + A = 9 + 10A + (7 - A)70 -10A +A = 9 + 10A + 7 - A70 - 9A = 9A + 1654 = 18AA = 3 and therefore B = 4 and the two-digit number is 34