# Potatoes 6

The farmer brought potatoes to the market. In the first hour, he sold two-fifths of the potatoes, in the second hour, he sold five-sixth of the remaining potatoes, and in the third hour, he had sold the last 40kg of potatoes. How many kilograms of potatoes did he sell in the second hour? How many kg did you bring to the market?

b =  200 kg
x =  400 kg

### Step-by-step explanation:

a = 2/5 x
b = 5/6 ·(x-a)
c = 40
x = a+b+c

a = 2/5·x
b = 5/6 ·(x-a)
c = 40
x = a+b+c

5a-2x = 0
5a+6b-5x = 0
c = 40
a+b+c-x = 0

Row 2 - Row 1 → Row 2
5a-2x = 0
6b-3x = 0
c = 40
a+b+c-x = 0

Row 4 - 1/5 · Row 1 → Row 4
5a-2x = 0
6b-3x = 0
c = 40
b+c-0.6x = 0

Row 4 - 1/6 · Row 2 → Row 4
5a-2x = 0
6b-3x = 0
c = 40
c-0.1x = 0

Row 4 - Row 3 → Row 4
5a-2x = 0
6b-3x = 0
c = 40
-0.1x = -40

x = -40/-0.1 = 400
c = 40/1 = 40
b = 0+3x/6 = 0+3 · 400/6 = 200
a = 0+2x/5 = 0+2 · 400/5 = 160

a = 160
b = 200
c = 40
x = 400

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