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Word problem involving the least common multiple of 2 numbers Suppose that hot dogs come in packs of 9 and buns come in packs of 12 . Sam bought the same number of hot dogs as buns. It was the least number of each for which this was possible. Answer the following questions. How many hot dogs did he buy? How many packs of hot dogs did he buy? How many packs of buns did he buy? \( \square \) packs Explanation

Ask by Flynn Martinez. in the United States
Mar 14,2025

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Sam bought 36 hot dogs in total. He bought 4 packs of hot dogs and 3 packs of buns.

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Beyond the Answer

To find the least number of hot dogs and buns Sam could buy, we need to determine the least common multiple (LCM) of 9 and 12. The multiples of 9 are 9, 18, 27, 36, and so on. The multiples of 12 are 12, 24, 36, and so on. The smallest common multiple is 36. Therefore, Sam bought 36 hot dogs and 36 buns. Now, to find out how many packs Sam bought: For hot dogs: \(36 \div 9 = 4\) packs. For buns: \(36 \div 12 = 3\) packs. So, Sam bought 36 hot dogs, which means he bought \(4\) packs of hot dogs and \(3\) packs of buns. \( \boxed{4} \) packs

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