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

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

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

Hence the number of boys in the course are: 224