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In a class, 2/3 of the students are girls. 1/4 of the girls are asleep, and 2/5 of the boys are asleep. What fraction of the class is awake.

This is what I did:

Let $x%$ be the total number of students.

Thus the number of girls is $\frac{2}{3}x$ and the number of boys is $\frac{1}{3}x$.


Since $1/4$ of the girls are asleep, the number of sleeping girls is $\frac{2}{3}\cdot \frac{1}{4}x\; =\; \frac{1}{6}x$

Similarly, the number of sleeping boys is $\frac{1}{3}\cdot \frac{2}{5}x\; =\; \frac{2}{15}x$


Since $\frac{1}{6}x$ is the number of sleeping girls, $\frac{5}{6}x$ is the number of girls that are awake. Similarly, since the number of sleeping boys is $\frac{2}{15}x$, the number of boys that are awake is $\frac{13}{15}x$.

This gives a total of $\frac{13}{15}x + \frac{5}{6}x$ sleeping students, but this simplifies to $\frac{17}{10}x$, and that is obviously wrong.


Where did I make a mistake?

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Number of girls, who are awake is not $x- \dfrac{x}6$. It is $\color{red}{\dfrac{2x}{3}} - \dfrac{x}6$.

Similarly, number of boys, who are awake is not $x- \dfrac{2x}{15}$. It is $\color{blue}{\dfrac{x}{3}} - \dfrac{2x}{15}$.

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  • $\begingroup$ Oops. Seems obvious now... $\endgroup$ – 1110101001 Dec 17 '13 at 0:22

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