Question

A teacher bought 32 notebooks, 72 pencils and 24 erasers to make identical packages with some notebooks, some pencils and some erasers for his students. He used everything he bought, and every student got a package. What is the largest number of students the teacher can have in his class? How many notebooks, pencils, erasers would be in each package?

Answer 1

I think that if they are all identical packages at most there are 8 class members. I am thinking that the answer is 8 because 8 is the greatest common factor between all three numbers(24,32,72).

Cannot go higher with out giving half a pencil to someone.Or 1/3 of a notebook.
But, all the numbers are divisible by 8.

So, each of the 8 students would get in their package:
72/8= 9 pencils
32/8= 4 notebooks
24/8= 3 erasers

Final Answer: 8 people at most are in this class and each student receives an identical package containing 4 notebooks, 9pencils, and 3 erasers.

Hope this helped! Comment with any questions you still have on this!

Answer 2

Given that a teacher bought 32 notebooks, 72 pencils and 24 erasers to make identical packages with some notebooks, some pencils and some erasers for his students.

Given that he used everything he bought, and every student got a package the largest number of students the teacher can have in his class represents the highest common factor of 32, 72 and 24.

32 = 2 x 2 x 2 x 2 x 2
72 = 2 x 2 x 2 x 3 x 3
24 = 2 x 2 x 2 x 3

HCF = 2 x 2 x 2 = 8

Therefore, the largest number of students the teacher can have in his class is 8 students.

The number of notebooks in each package is given by 32 / 8 = 4 notebooks.
The number of pencils in each package is given by 72 / 8 = 9 pencils
The number of erasers in each package is given by 24 / 8 = 3 erasers