[2/3 Points] DETAILS TGEIALG6 2.5.051. The three numbers of the combination for a lock are consecutive integers, and their sum is 99. Find the combination. smallest value largest value SUBMIT ANSWER
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Did you know that the ancient Romans used combination locks to protect their valuables? These intricate devices required users to align various parts in a specific order to unlock them, much like solving a puzzle! Now, let’s solve this riddle! Since the numbers are consecutive integers, let's call them \( x \), \( x+1 \), and \( x+2 \). The equation based on their sum would be \( x + (x + 1) + (x + 2) = 99 \). Simplifying that gives us \( 3x + 3 = 99 \), leading to \( 3x = 96 \), giving \( x = 32 \). So, the combination is 32, 33, and 34!