Badminton

On Friday, there was a sports day at school, attended by several students. A third of these students participated in a badminton tournament, a quarter of the remaining number threw a cricket ball, two-thirds of the remaining number competed in running and the remaining seven students competed in long jump. How many students participated in the sports day?

Correct answer:

x =  42

Step-by-step explanation:

$$\begin{gathered} a=\frac{1}{3}\doteq 0.3333 \\ b=(1-a)/4=(1-\frac{1}{3})/4=\frac{1}{6}\doteq 0.1667 \\ c=\frac{2}{3}\cdot (1-a-b)=\frac{2}{3}\cdot (1-\frac{1}{3}-\frac{1}{6})=\frac{1}{3}\doteq 0.3333 \\ a\cdot x+b\cdot x+c\cdot x+7=x \\ \frac{1}{3}\cdot x+\frac{1}{6}\cdot x+\frac{1}{3}\cdot x+7=x \\ 1/3\cdot x+1/6\cdot x+1/3\cdot x+7=x \\ x=42 \\ x=\frac{42}{1}=42 \\ x=42 \end{gathered}$$

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