There were 93 students going to a nature camp. After equal groups of fewer than10 students , were formed for hiking, 2 students were left over . How many equal groups were formed?
After 93 was divided by some number n, the remainder was 2, so clearly n >2
Divisor - remainder
3 ...... 0
4 ...... 1
5 ........ 3
6 ........3
7 ....... 2 yeahh
they formed 13 groups of 7 , leaving 2 students left over
If two students were left, there are 93-2=91 students who were in groups of equal size.
Find factors of 91 and you will have a choice of two, one of which is under 10, which is also the number of students per group. The other factor (greater than 10) is therefore the number of groups formed.
To solve this problem, we need to find the number of equal groups that were formed.
We know that there were 93 students going to the nature camp.
After forming equal groups of fewer than 10 students, 2 students were left over.
Let's first subtract the 2 students who were left over from the total number of students:
93 - 2 = 91
Now, to find the number of equal groups, we need to divide the remaining students by the maximum number of students in each group (which is fewer than 10).
Since we don't know the exact number of students in each group, we'll try different options until we find the answer.
Let's start by assuming that each group has 9 students:
91 ÷ 9 = 10 remainder 1
This means that if each group has 9 students, we will have 10 groups with 1 student left over.
Now, let's try the next option of each group having 8 students:
91 ÷ 8 = 11 remainder 3
If each group has 8 students, we will have 11 groups with 3 students left over.
We can keep trying different options until we find the number of equal groups where the remainder is 2 (since we know that 2 students were left over).
Continuing this process, we find that:
91 ÷ 7 = 13 remainder 0
91 ÷ 6 = 15 remainder 1
91 ÷ 5 = 18 remainder 1
91 ÷ 4 = 22 remainder 3
91 ÷ 3 = 30 remainder 1
91 ÷ 2 = 45 remainder 1
91 ÷ 1 = 91 remainder 0
Finally, we find that when we divide 91 by 5, we get a remainder of 2:
91 ÷ 5 = 18 remainder 1
Therefore, the number of equal groups that were formed is 18.
So, the answer is: 18 equal groups were formed.
To solve this problem, we need to find the number of equal groups that were formed with fewer than 10 students each.
Step 1: Subtract the number of students left over from the total number of students.
Total number of students - Students left over = Students divisible by the group size
93 - 2 = 91
Step 2: Determine the possible group sizes by finding the factors of the number of students divisible by the group size.
Factors of 91: 1, 7, 13, 91
Step 3: Since we are looking for groups with fewer than 10 students, we can eliminate 13 and 91 as potential group sizes.
Step 4: Test the remaining factors to see if they satisfy the condition of having fewer than 10 students per group.
Group size 1: 91 students / 1 = 91 groups (not fewer than 10)
Group size 7: 91 students / 7 = 13 groups (fewer than 10)
Therefore, the number of equal groups that were formed is 13.