# Potatoes 6

The farmer brought potatoes to the market. In the first hour he sold two-fifths of the potatoes brought, 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 kg of potatoes did he sell in the second hour? How many kg did you brought 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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