To solve this problem, let’s start by identifying the requirements. We need to evenly distribute 180 books and 50 pens among a certain number of students, such that each student gets the same number of books and the same number of pens without having any leftover.
We have four possible choices for the number of students: 20, 10, 36, and 900. We will need to check which of these numbers can evenly divide both the total number of books and the total number of pens.
1. Choice A) 20:
- For books: 180 ÷ 20 = 9, which is an integer.
- For pens: 50 ÷ 20 = 2.5, which is not an integer.
- Since pens cannot be evenly distributed among 20 students, 20 is not a valid choice.
2. Choice B) 10:
- For books: 180 ÷ 10 = 18, which is an integer.
- For pens: 50 ÷ 10 = 5, which is an integer.
- Both the books and the pens can be evenly distributed among 10 students.
- Therefore, 10 is a valid choice.
3. Choice C) 36:
- For books: 180 ÷ 36 = 5, which is an integer.
- For pens: 50 ÷ 36 ≈ 1.3889, which is not an integer.
- Since pens cannot be evenly distributed among 36 students, 36 is not a valid choice.
4. Choice D) 900:
- For books: 180 ÷ 900 = 0.2, which is not an integer.
- For pens: 50 ÷ 900 ≈ 0.0556, which is also not an integer.
- Since neither the books nor the pens can be evenly distributed among 900 students, 900 is not a valid choice.
After evaluating all the options, we find that the only choice that allows for both the books and the pens to be evenly distributed among the students is:
10 students.
Therefore, the correct answer is:
B) 10.
