Mr. D. O. Nutt brought a baker’s dozen, or 13, pastries to the math department meeting. Everyone ate at least 1 pastry, some (not all) had 2, and one person had 3. What are the possible numbers of people who could be in the department?
13 - 3 = 10 for (n-1) people
10 - 2 = 8 for (n-2) people if one has 2
so if (n -2) people eat 1 each, then n-2 = 8 and there are max of 10 people
but (n-2) people might eat 2 each so in that case there would only be 4 of them and n - 2 = 4 so n = 6
so
6 min and 8 max but 7 is hard unless you cut a pastry in half
The sum of two numbers 43 and their difference is 35.find the numbers.
To solve this problem, we can start by considering the maximum number of pastries consumed, which is when everyone had 3 each. In this case, if we divide the total number of pastries (13) by 3, we get 4.333. However, since we can't have a fraction of a person, this means that there cannot be 4 or fewer people in the department.
Now, let's consider the minimum number of pastries consumed, which is when everyone had just 1 each. In this case, we can distribute 13 pastries among the people in the department equally. So, the minimum number of people in the department would be 13.
Therefore, the possible numbers of people who could be in the department range from 5 to 13.