Question

In a school, $\frac{5}{8}$ of the students are boys. If there are 240 girls, find the number of boys in the school.

Answer 1

If $\frac{5}{8}$of the students are boys, then the ratio of girls is $1-\frac{5}{8}$, that is, $\frac{3}{8}$.

Now, let x be the total number of students.

Thus, we have:

$$\begin{gathered} \frac{3}{8}x=240 \\ \Rightarrow x=240÷\frac{3}{8} \end{gathered}$$

$$\begin{gathered} =240\times \frac{8}{3} \\ =\frac{240}{1}\times \frac{8}{3} \\ =\frac{240\times 8}{1\times 3} \\ =\frac{1920}{3} \\ =640 \end{gathered}$$

Hence, the total number of students is 640.
Now,
Number of boys = Total number of students - Number of girls
$$\begin{gathered} =640-240 \\ =400 \end{gathered}$$

Hence, the number of boys is 400.