Please Help! 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.

36 is the correct answer.

Step-by-step explanation:

It is given that there are a group of tourists that can be sorted in a group of either 4 or 6 so that there are no empty seats.

It means that the total number of seats should be a multiple of both 4 and 6.

For finding such a number we can simply find out LCM (Least Common Multiple) of 4 and 6.

LCM of two numbers p and q is the minimum number which can be completely divided by both the numbers p and q.

Let us find the LCM of 4 and 6 here, using the factors:

4 = 2 2

6 = 2 3

The common factor(shown as underlined) is used only once in the LCM.

So, LCM =  2 2 3 = 12

So, 12 is the minimum number which can be divided by 4 and 6 both.

But, we are given a condition that number of tourists are more than 25 and lesser than 45. So, the number of seats can be in between 25 and 45.

Now, let us see multiples of 12:

12, 24, 36, 48, 60, ......

The number that lies between 25 and 45 is 36.

So, the number of total seats can be 36.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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