Running race

A running race consists of two stages. Two thirds of the competitors completed the first stage, and only three quarters of those completed the second stage. Only 12 competitors reached the finish line. Determine how many competitors started and how many did not even complete the first stage.

Final 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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