Problems from Percentages

Development:

It is a question of applying rules of three to know the percentage of every result.

In the case of the passes: $\begin{array}{rcl}5& \to & 8\\ \\ x& \to & 100\end{array}$

So,he has passed $5$ of $8$, which represents a $x$ per cent.

Expressed in fractions it is:

${\displaystyle \frac{5}{x}}={\displaystyle \frac{8}{100}}\Rightarrow 8x=5\cdot 100\Rightarrow 8x=500\Rightarrow x={\displaystyle \frac{500}{8}}=62,5\mathrm{\%}$

In case of the failures: $\begin{array}{rcl}3& \to & 8\\ \\ x& \to & 100\end{array}$

Otherwise:

${\displaystyle \frac{3}{x}}={\displaystyle \frac{8}{100}}\Rightarrow 8x=3\cdot 100\Rightarrow 8x=300\Rightarrow x={\displaystyle \frac{300}{8}}=37,5\mathrm{\%}$

It was possible to find the same value by substracting the entire percentage of passes from $100\mathrm{\%}$:

$100-62,5=37,5\mathrm{\%}$

Solution:

The percentage of passes is $62,5\mathrm{\%}$ and the one of failures is $37,5\mathrm{\%}$.

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