Percentage - fence

We are painting a wooden fence. On the first day, we painted one-half of the fence. The next day, we painted half of the remaining part. On the third day, again, half of the remaining part. After the third painting, we had 12.5 meters of unpainted fence left. How long is the entire fence? What percentage of the fence will we have painted in three days?

Final Answer:

x =  100 m

Step-by-step explanation:

$$\begin{gathered} a=\frac{1}{2}=0.5 \\ b=\frac{1}{2}\cdot (1-a)=\frac{1}{2}\cdot (1-\frac{1}{2})=\frac{1}{4}=0.25 \\ c=\frac{1}{2}\cdot (1-a-b)=\frac{1}{2}\cdot (1-\frac{1}{2}-\frac{1}{4})=\frac{1}{8}=0.125 \\ r=a+b+c=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}=\frac{4}{8}+\frac{2}{8}+\frac{1}{8}=\frac{4+2+1}{8}=\frac{7}{8}=0.875 \\ x\cdot r+12.5=x \\ x\cdot 0.875+12.5=x \\ 0.125x=12.5 \\ x=\frac{12.5}{0.125}=100 \\ x=100=100\text{m} \end{gathered}$$

Try another example