We have $400$ students in a school. Every $20^{th}$ student failed at the end of the school year. Which was $2\%$ of schools girls and $10\%$ of schools boys.

The number of all boys attending the school is?

What I tried:

We know that every $20^{th}$ student fails, which means that $20$ students have failed. We also know that in these $20$ students are $2\%$ of all girls from the school and $10\%$ of all boys from the school. So we can make two equations like this: $$400 = b + g$$ $$20 = 0.1b + 0.02g$$

--I know the answer is $150$, but I got a different one.. if someone could point out an error in my logic, or just show how to solve it?


Your equations are correct, so you apparently just made a mistake in solving the system.

I’d multiply the second equation by $10$ to get $200=b+0.2g$ and then subtract that from the first equation to get $200=0.8g$. Then $g=250$, so $b=400-250=150$.

  • $\begingroup$ Yeah, I made a stupid mistake, thanks :) $\endgroup$ – Mykybo Apr 10 '15 at 21:02
  • $\begingroup$ @Mykybo: It happens. You’re welcome! $\endgroup$ – Brian M. Scott Apr 10 '15 at 21:07

In your equation replace $g = 400 - b$ then you will get $b = 150$.


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