The ratio of men to women is $3:4$, the ratio of Americans to non-Americans is $7:2$, and the number of people that are in the room is less than $100$. How many people are in the room?
I am helping my younger brother out with math and, sadly, I don't remember how to do this. Could someone please give me a quick refreshing on this?
P.S. I don't even know where to start - and I don't know exactly what this is called so I can't search it in order to find steps to solve this answer.
Thanks for your time!
As the number of men and american's in the room are both natural numbers, total number of people in the room must be divisible by both $(3+4)=7$ and $(7+2)=9$.
Now, $lcm(7,9)=63$.
We are told that the number of people in the room is less than 100. Hence, number of people in the room is exactly $63$. As the next number, after $63$, which is divisible by $7$ and $9$ both is $63\times 2=126>100$.