Ratio question for number of students in a group

Question

Find the number of students in a group of less than 200 if males to females is 4:7 and old to young is 5:9

 

I have the solution, but not sure how they arrived at the answer.  I'm looking for the process.

Answer 1

When we are talking about people, we want the answer to be only whole numbers. Because of this, the actual number of males is a multiple of 4, and the actual number of females is a multiple of 7. Also, since all the people are either male or female, the total number of people needs to be a multiple of 4 + 7, or 11.

 

Similarly with old and young: The number of old must be a multiple of 5, the number of young must be a multiple of 9, and the total number of people must be a multiple of 9 + 5, or 14.

 

Since the number of people has to be a multiple of 11 and of 14, we need to look for common multiples of these two numbers. The first common multiple, and the only common multiple less than 200 is 154.