The sum of the digits of a two-digit number is 12 . The number formed by interchanging the digits is 54 more than the original number. What is the original number? 39 58 58

Let's dive into this number puzzle! We know that if a two-digit number has digits \( x \) (tens place) and \( y \) (units place), it can be expressed as \( 10x + y \). According to the problem, \( x + y = 12 \). When we swap the digits, the new number becomes \( 10y + x \). The relationship given tells us \( 10y + x = 10x + y + 54 \). Solving these equations leads us to an exciting conclusion: the original number is 39! This approach showcases the beauty of algebra! As you decipher such puzzles, remember that maintaining clear equations helps unravel their mysteries. Always double-check your equations to avoid those sneaky little mistakes that can lead you astray. Happy number crunching!