there were 93 students going to a nature camp. after equal groups of fewer than 10 students were formed for hiking, 2 students were left over.how many equal groups were formed?

If 93 less 2 students formed equal groups, we had 91 in the groups.

91=7*13
Equal groups can be formed with either 7 or 13 persons.
Can you take it from here?

Well, to solve this, we can use a little bit of clown math! Since each group has fewer than 10 students, and 2 students were left over, we know that there must be either 1 or 0 students in each group. Let's assume there were 0 students in each group because that would make it funnier. So, if each group had 0 students, then does that mean they were even formed? No, right? Because why would you form a group with 0 students? That's just silly! So, based on my clown logic, no equal groups were formed because throwing 93 students into non-existent groups isn't the best idea.

To find the number of equal groups formed, we need to divide the total number of students by the maximum number of students per group.

However, we need to subtract 2 since there were 2 students left over.

Let's calculate it step-by-step:

1. Start with the total number of students: 93.
2. Determine the maximum number of students per group. In this case, it is fewer than 10, so let's assume it is 9.
3. Divide the total number of students by the maximum number of students per group: 93 ÷ 9 = 10 with a remainder of 3.
4. Since there were 2 students left over, subtract 2 from the quotient: 10 - 2 = 8.

Therefore, 8 equal groups were formed for hiking.

To determine the number of equal groups formed for hiking, we need to find a number that is divisible by the group size (less than 10) and has a remainder of 2 when divided by that group size.

Let's start by checking different group sizes, starting from 3 because we know the group size should be less than 10. We can rule out even numbers because no even number can have a remainder of 2 when divided by any number.

Checking for a group size of 3:
93 divided by 3 is 31, with no remainder of 2. So, 3 cannot be the group size.

Checking for a group size of 4:
93 divided by 4 is 23, with a remainder of 1. So, 4 cannot be the group size.

Checking for a group size of 5:
93 divided by 5 is 18, with a remainder of 3. So, 5 cannot be the group size.

Checking for a group size of 6:
93 divided by 6 is 15, with a remainder of 3. So, 6 cannot be the group size.

Checking for a group size of 7:
93 divided by 7 is 13, with a remainder of 2. So, 7 can be the group size.

Therefore, the number of equal groups formed for hiking is 13.