A teacher is making back to school supply gifts for his students. He has 72 pencils and 96 erasers. If he is giving each student the same number of pencils and the same number of erasers, how many students are in his class? He will have no extra bags after he distributes them
There are 24 students in the teacher's class.
24
To find out the number of students in the class, we need to divide the total number of pencils by the number of pencils each student will receive. We can do the same for erasers and compare the results.
First, let's find out how many pencils each student will receive. Since the teacher wants to distribute all the pencils without any extras, the number of pencils each student receives should be a factor of 72. We can start dividing 72 by different numbers to see which ones divide evenly.
72 ÷ 1 = 72
72 ÷ 2 = 36
72 ÷ 3 = 24
72 ÷ 4 = 18
72 ÷ 5 = 14.4 (not a whole number)
72 ÷ 6 = 12
72 ÷ 8 = 9 (perfect!)
So, each student will receive 8 pencils.
Now, let's find out how many erasers each student will receive. Again, we want to distribute all the erasers without any extras, so the number of erasers each student receives should also be a factor of 96.
96 ÷ 1 = 96
96 ÷ 2 = 48
96 ÷ 3 = 32
96 ÷ 4 = 24
96 ÷ 6 = 16
96 ÷ 8 = 12 (perfect!)
So, each student will receive 12 erasers.
Since we are giving the same number of pencils and erasers to each student, we take the lowest common multiple (LCM) of 8 and 12 to find the total number of supplies each student will receive.
The LCM of 8 and 12 is 24, so each student will receive 24 supplies.
To find the number of students in the class, we divide the total number of pencils (72) or the total number of erasers (96) by 24:
72 ÷ 24 = 3
96 ÷ 24 = 4
Therefore, there are either 3 or 4 students in the class, as both numbers are factors of both 72 and 96.