Repairing 80759

They spent three days repairing the damaged pipe, 115 m long. On the first day, they repaired a quarter of what they did on the second day, and on the third day, they repaired 20m less than on the second day. How many m of pipe did they repair on the first, second, and third day?

Correct answer:

a =  15 m
b =  60 m
c =  40 m

Step-by-step explanation:

$$\begin{gathered} a+b+c=115 \\ a=b/4 \\ c=b-20 \\ a+b+c=115 \\ 4a-b=0 \\ b-c=20 \\ Pivot:Row1\leftrightarrow Row2 \\ 4a-b=0 \\ a+b+c=115 \\ b-c=20 \\ Row2-\frac{1}{4}\cdot Row1\to Row2 \\ 4a-b=0 \\ 1.25b+c=115 \\ b-c=20 \\ Row3-\frac{1}{1.25}\cdot Row2\to Row3 \\ 4a-b=0 \\ 1.25b+c=115 \\ -1.8c=-72 \\ c=\frac{-72}{-1.8}=40 \\ b=\frac{115-c}{1.25}=\frac{115-40}{1.25}=60 \\ a=\frac{0+b}{4}=\frac{0+60}{4}=15 \\ a=15 \\ b=60 \\ c=40 \end{gathered}$$

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