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 must be______students in his class.
To find the number of students in the class, we need to divide the total number of pencils and erasers by the number of each item given to each student.
Since each student receives the same number of pencils and erasers, we can divide both quantities by the number of items given to each student.
When we divide 72 pencils by the number of pencils given to each student, we obtain 96 erasers divided by the number of erasers given to each student.
72 pencils ÷ number of pencils per student = 96 erasers ÷ number of erasers per student.
Let's call the number of pencils and erasers given to each student "x".
72 pencils ÷ x = 96 erasers ÷ x.
To make the equation simpler, we can multiply both sides by x:
72 pencils = 96 erasers.
Since there are no other items mentioned, we can assume that x represents the number of pencils and erasers given to each student. Therefore, a student receives 72 pencils and 96 erasers.
Now, we need to find the number of students in the class. We can divide the total number of pencils by the number of pencils given to each student.
Number of students = 72 pencils ÷ number of pencils per student.
= 72 pencils ÷ 72 pencils per student.
= 1 student.
Therefore, there is 1 student in his class.
Are you sure?
Apologies for the incorrect response. Allow's solve the problem correctly:
Let's assume the number of pencils and erasers given to each student as "x".
We know that there are 72 pencils and 96 erasers available.
To find the number of students, we need to divide the total number of pencils (72) by the number of pencils given to each student (x):
Number of students = 72 pencils ÷ number of pencils per student
We also need to divide the total number of erasers (96) by the number of erasers given to each student (x):
Number of students = 96 erasers ÷ number of erasers per student
Since the number of students must be the same in both cases (as they are the same group of students), we can equate these two expressions:
72 pencils ÷ x = 96 erasers ÷ x
To solve for "x", we can cross-multiply:
72x = 96x
Subtracting 72x from both sides, we get:
0 = 24x
Dividing both sides by 24, we find:
0 = x
According to this solution, the number of pencils and erasers given to each student would be zero. However, this is not possible, as each student is expected to receive some supplies.
Therefore, there is no solution that satisfies the given conditions. It seems there is an error in the information provided, as the current quantities of pencils and erasers cannot be evenly distributed among the students without any remainder.