The Correct Answer and Explanation is:
60
This problem asks for the first time that the baking cycles for scones, muffins, and cookies will all finish simultaneously. This is a classic math problem that requires finding the least common multiple (LCM) of the three different baking times.
First, we must identify the baking time for each item. The problem states that muffins bake for 12 minutes and cookies bake for 10 minutes. The baking time for the scones is difficult to read from the image, but based on common versions of this problem, it is 15 minutes. The process described is continuous; as soon as one tray is removed, another of the same item is put in its place. This creates repeating cycles for each baked good.
The scones will be ready to be removed at intervals of 15 minutes.
The muffins will be ready to be removed at intervals of 12 minutes.
The cookies will be ready to be removed at intervals of 10 minutes.
To find the first moment when all three are ready at the same time, we need to find the smallest number that is a multiple of 15, 12, and 10. This is the least common multiple.
We can find the LCM by listing the multiples of each number until we identify the first one they all share.
- Multiples of 15: 15, 30, 45, 60, 75, 90, …
- Multiples of 12: 12, 24, 36, 48, 60, 72, 84, …
- Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, …
By examining the lists, we can see that 60 is the first number that appears in all three sequences. This means that at the 60 minute mark, a tray of scones, a tray of muffins, and a tray of cookies will have just completed their baking cycles. Therefore, 60 minutes is the first time after starting that Caylan will remove all three items from the oven at the same time.
