Rope

Half of the rope used Mam for packaging, half of the rest got a son, half of the rest he took the father and two-fifths of what remained and got a daughter. Remained 69 cm of rope.

How long was the rope at the beginning?

Final Answer:

x =  920 cm

Step-by-step explanation:

$$\begin{gathered} a=\frac{1}{2}=0.5 \\ b=\frac{1}{2}\cdot (1-a)=\frac{1}{2}\cdot (1-0.5)=\frac{1}{4}=0.25 \\ c=\frac{1}{2}\cdot (1-a-b)=\frac{1}{2}\cdot (1-0.5-0.25)=\frac{1}{8}=0.125 \\ d=\frac{2}{5}\cdot (1-a-b-c)=\frac{2}{5}\cdot (1-0.5-0.25-0.125)=\frac{1}{20}=0.05 \\ x-a\cdot x-b\cdot x-c\cdot x-d\cdot x=69 \\ x-0.5\cdot x-0.25\cdot x-0.125\cdot x-0.05\cdot x=69 \\ 0.075x=69 \\ x=\frac{69}{0.075}=920 \\ x=920=920\text{cm} \end{gathered}$$

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