Question

There are 416 students who are enrolled in an introductory geology course. if there are seven boys to every six girls, how many boys are in the course

Answer 1

`\text{Let the number of boys be x and number of girls be y.}\\ \\ \text{and there are total 416 students enrolled in the course. so we have}\\ \\ x+y=416 \ \ \ \ \ \ \ \ \ \ ......(i)\\ \\ \text{also given that there are seven boys to every six girls, that is}\\ \\ (x)/(y)=(7)/(6)`

`\Rightarrow 6x=7y\\ \\ \Rightarrow y=(6x)/(7)\\ \\ \text{substitute this value of y in (i), we get}\\ \\ x+(6x)/(7)=416\\ \\ \Rightarrow (7x+6x)/(7)=416\\ \\ \Rightarrow (13x)/(7)=416\\ \\ \Rightarrow x=(416* 7)/(13)\\ \\ \Rightarrow x=224`

Hence the number of boys in the course are: 224