Question

A group of tourists can be sorted into tour boats in groups of 4 or in groups of 6. In either case, there are no empty seats. Find the number of tourists if there are more than 25 and fewer than 45.

Answer 1

Answer: there are 36 tourists.

Explanation:

Ok, we have two integer numbers:

T, the number of tourists and S, the number of seats.

Such that, if we divide the tourists into groups of 4 and in groups of 6, we end with no empty seats.

Knowing that the number S must be an integer, and when we divide T into groups of 4 and 6 we end with no empty seats, this means that T can be divided by 4 and by 6.

This means that T is a common multiple of 4 and 6

Now, we also know that 25 < T < 45.

Then let's see which ones are the multiples of 4 between 25 and 45.

4*7 = 28

4*8 = 32

4*9 = 36

4*10 = 40

4*11 = 44.

Now, the multiples of 6 in that range are:

6*5 = 30

6*6 = 36

6*7 = 42.

You can see that 36 is a common multiple, other way to see it is:

4*9 = (2*2)*(3*3) = 2*2*3*3 = (2*3)*(2*3) = 6*6

So the numer of tourist must be 36.