Kaylan is making baked goods for a charity bake sale. He places a tray of scones, a tray of muffins, and a tray of cookies in the oven. The scones bake for 15 minutes, the muffins bake for 12 minutes, and the cookies bake for 10 minutes. When one tray is done, he removes it and replaces it with another tray of the same item. How many minutes after Kaylan puts the trays in the oven will he first remove the scones, muffins, and cookies at the same time?

Question

03-01-2025
Mathematics

High School

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Kaylan is making baked goods for a charity bake sale. He places a tray of scones, a tray of muffins, and a tray of cookies in the oven. The scones bake for 15 minutes, the muffins bake for 12 minutes, and the cookies bake for 10 minutes. When one tray is done, he removes it and replaces it with another tray of the same item. How many minutes after Kaylan puts the trays in the oven will he first remove the scones, muffins, and cookies at the same time?

Answer :

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KurtDavies KurtDavies · Answer 1 · 2023-12-16T09:34:16-05:00

The least common multiple of the baking times for scones (15 minutes), muffins (12 minutes), and cookies (10 minutes) is 60 minutes. Therefore, after 60 minutes, Kaylan will first remove all the trays simultaneously from the oven.

The question here is focused on finding the least common multiple (LCM) of the baking times for scones, muffins, and cookies to determine when Kaylan will first remove all of them from the oven simultaneously. Each item has a specific baking time: scones take 15 minutes, muffins take 12 minutes, and cookies take 10 minutes. To solve this, we need to calculate the LCM of these three numbers.

To find the LCM, we can list the multiples of each baking time:

15: 15, 30, 45, 60, 75, 90, ...
12: 12, 24, 36, 48, 60, 72, ...
10: 10, 20, 30, 40, 50, 60, ...

Upon examination of these lists, the smallest multiple they all share is 60 minutes. Therefore, after 60 minutes, Kaylan will first be able to remove the scones, muffins, and cookies from the oven at the same time.