Reservoir volume calculation

The three water reservoirs hold a total of 130 liters. Determine their volumes in m³. If the first fits 15 liters less than the second and 20 liters less than the third.

Final Answer:

a =  0.04 m³
b =  0.055 m³
c =  0.035 m³

Step-by-step explanation:

$$\begin{gathered} V_1=130\text{l}\to {\text{m}}^3=130:1000{\text{m}}^3=0.13{\text{m}}^3 \\ a+b+c=V_1 \\ a=b-15/1000 \\ c=b-20/1000 \\ a+b+c=0.13 \\ a+b+c=0.13 \\ 1000a-1000b=-15 \\ 1000b-1000c=20 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{1000}\cdot Row1\to Row2 \\ 2b+c=0.145 \\ Pivot:Row2\leftrightarrow Row3 \\ Row3-\frac{2}{1000}\cdot Row2\to Row3 \\ 3c=0.105 \\ c=\frac{0.105}{3}=0.035 \\ b=\frac{20+1000c}{1000}=\frac{20+1000\cdot 0.035}{1000}=0.055 \\ a=\frac{-15+1000b}{1000}=\frac{-15+1000\cdot 0.055}{1000}=0.04 \\ a=\frac{1}{25}=0.04 \\ b=\frac{11}{200}=0.055 \\ c=\frac{7}{200}=0.035 \end{gathered}$$

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