Mountains 57433

The trip to the seaside vacation was as follows:
80% of the entire route was on the plain.
40% of the rest was through the mountains.
The remaining 180 km was along the coast.
What is the total length of the route? Thank you

Correct answer:

x =  1500 km

Step-by-step explanation:

$$\begin{gathered} p_1=80\%=\frac{80}{100}=\frac{4}{5}=0.8 \\ {p}_2=40\%=\frac{40}{100}=\frac{2}{5}=0.4 \\ {p}_3=(1-p_1)\cdot p_2=(1-0.8)\cdot 0.4=\frac{2}{25}=0.08 \\ {p}_1\cdot x+p_3\cdot x+180=x \\ 0.8\cdot x+0.08\cdot x+180=x \\ 0.12x=180 \\ x=\frac{180}{0.12}=1500 \\ x=1500=1500\text{km} \end{gathered}$$

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