Question:
Old Mr. Baker was known for his impeccable calculations. He had a small bakery, and every day, he meticulously recorded the number of loaves he baked. One week, he found the average number of loaves baked per day was thirteen. Determined to maintain his bakery's reputation for consistency, he decided to include the next day's loaf count in his average. However, he wanted to ensure the average for the six days remained a whole number. What was the smallest number of loaves he could bake on the sixth day to achieve this?
Old Mr. Baker was known for his impeccable calculations. He had a small bakery, and every day, he meticulously recorded the number of loaves he baked. One week, he found the average number of loaves baked per day was thirteen. Determined to maintain his bakery's reputation for consistency, he decided to include the next day's loaf count in his average. However, he wanted to ensure the average for the six days remained a whole number. What was the smallest number of loaves he could bake on the sixth day to achieve this?
Updated On: Aug 20, 2024
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The Correct Option is D
Solution and Explanation
Total loaves for the first 5 days = 5\(\times\) 13 = 65 loaves.
Let the number of loaves on the 6th day be x.
Total loaves for all 6 days = 65 + x.
For the average to be a whole number, the total loaves for all 6 days should be divisible by 6.
So, 65 + x should be a multiple of 6.
The smallest multiple of 6 greater than 65 is 66.
Therefore, 65 + x = 66.
Solving for x, we get x = 1.
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