The farmer

The farmer brought potatoes to the market. In the first hour, he sold two-fifths of the potatoes brought in. He sold five-sixths of the remaining potatoes in the second hour, and in the third hour, he sold the last 40 kg of potatoes.

1. Express a fraction of what portion is left after the first sale hour.
2. Calculate how many kilograms of potatoes the farmer sold in the second hour.
3. Calculate how many kilograms of potatoes the farmer brought to the market.

Final Answer:

a =  3/5
b =  200 kg
c =  400 kg

Step-by-step explanation:

$a=1-\frac{2}{5}=\frac{1\cdot 5}{5}-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}=0.6$

$$\begin{gathered} \frac{2}{5}c+b+40=c \\ b=\frac{5}{6}(c-\frac{2}{5}c) \\ 2/5\cdot c+b+40=c \\ b=5/6\cdot (c-2/5\cdot c) \\ 5b-3c=-200 \\ 30b-15c=0 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{5}{30}\cdot Row1\to Row2 \\ -0.5c=-200 \\ c=\frac{-200}{-0.5}=400 \\ b=\frac{0+15c}{30}=\frac{0+15\cdot 400}{30}=200 \\ b=200 \\ c=400 \end{gathered}$$

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