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5 January, 16:27

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.

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  1. 5 January, 16:36
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    Answer: there are 36 tourists.

    Step-by-step 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.
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