Question

There are five boys to every three girls in an introductory chinese course. if there are 384 students enrolled in the course, how many are boys?

Answer 1

There are 240 boys.

Explanation:

There are five boys to every three girls in an introductory Chinese course. Given that there are 384 students enrolled in total, we want to determine the amount of students which are boys.

Let b represent the number of boys and g girls.

Since the ratio is 5:3, we can write that:

`\displaystyle (5)/(3) = (b)/(g)`

And since the total number of students is 384:

`b + g = 384`

From the first equation, cross-multiply:

`5g = 3b`

Solve for g:

`\displaystyle g = (3)/(5) b`

Substitute:

`\displaystyle b + \left ((3)/(5) b\right) = 384`

Simplify:

`\displaystyle (8)/(5) b = 384`

Solve for b:

`\displaystyle b = (5)/(8)\left(384\right) = 240`

In conclusion, 240 of the total students are boys.