Running race

The running race consists of two stages. Two-thirds of the competitors completed the first stage, and only three-quarters of them completed the second stage. Only 12 competitors reached the finish line. Determine how many competitors were at the start and how many did not even finish the first stage.

Correct answer:

n =  24
x =  8

Step-by-step explanation:

$$\begin{gathered} \frac{2}{3}\cdot \frac{3}{4}\cdot n=12 \\ n=12\cdot \frac{3\cdot 4}{2\cdot 3}=24 \end{gathered}$$

$x=\frac{1}{3}\cdot n=\frac{1}{3}\cdot 24=\frac{1\cdot 24}{3}=\frac{24}{3}=8$

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