A two-digit number has digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Find the number.
36
36 is correct.
Let the two-digit number be \(10a + b\) with \(a + b = 9\). Adding 27 reverses the digits, so \(10a + b + 27 = 10b + a\).
Step 1 — Simplify: \(9b - 9a = 27\), giving \(b - a = 3\).
Step 2 — Solve with \(a + b = 9\): adding the two equations gives \(2b = 12\), so \(b = 6\) and \(a = 3\).
Step 3 — Original number is \(10(3) + 6 = 36\); verify: \(36 + 27 = 63\), which is 36 reversed.
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