The carpenters

The carpenters cut the beam. Half of the cut pieces were 1 meter long, a quarter of the pieces were two meters long, and they cut the remaining 8 meters of the beam into two equal parts.
- What was the length of the original beam?
- What part of the original beam was cut into meter pieces?

Correct answer:

a =  16 m
b =  1/4

Step-by-step explanation:

$$\begin{gathered} n/2+n/4+2=n \\ n=8 \\ n=\frac{8}{1}=8 \\ n=8 \\ {d}_1=n/2\cdot 1=8/2\cdot 1=4\text{m} \\ {d}_2=n/4\cdot 2=8/4\cdot 2=4\text{m} \\ {d}_3=8\text{m} \\ a=d_1+d_2+d_3=4+4+8=16\text{m} \end{gathered}$$

$b=d_1/a=4/16=\frac{1}{4}=0.25$

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