When a teacher divided her students into groups of four, she had three students remaining. when she divided them into groups of five, she had four students remaining. there were fewer than 40 students in the class. how many students could be in the class?

We want to find the number of students in the class, we will see that there are 39 students in that class.

Let's assume that there are N students.

We know that if we divide the students in groups of 4, we have 3 remaining students, then we know that:

N = 4*k + 3

Where k is an integer.

We also know that if we divide the students in groups of 5, there are 4 students remaining.

Then:

N = 5*c + 4

Where c is an integer.

Finally, we know that there are less than 40 students, then:

N < 40.

With this, we can find the number N.

Notice that all the multiples of 5 end in either 5 or 0.

If it ends in 5, when we add 4, it will end with a 9.

An example of this is:

5*7 + 4 = 39

Now we want to find a multiple of 4 that when we add 3 we get 39:

Similarly, we also have:

4*9 + 3 = 36 + 3 = 39

Then 39 students meet the two requirements, and also is smaller than 40, then the number of students in the class is 39.

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