# Coal storage

The coal storage distribution received coal shipment within three days. On the first day, distribute a third of the shipments, on the second day of two-fifths of the rest, and on the third day, 300 tons of coal. How many tons of coal were distributed first and second days?

a =  250 t
b =  200 t

## Step-by-step explanation:

a+b+300 = t
a = t/3
b = 2/5(t - a)

a+b+300 = t
a = t/3
b = 2/5·(t - a)

a+b-t = -300
3a-t = 0
2a+5b-2t = 0

Pivot: Row 1 ↔ Row 2
3a-t = 0
a+b-t = -300
2a+5b-2t = 0

Row 2 - 1/3 · Row 1 → Row 2
3a-t = 0
b-0.667t = -300
2a+5b-2t = 0

Row 3 - 2/3 · Row 1 → Row 3
3a-t = 0
b-0.667t = -300
5b-1.333t = 0

Pivot: Row 2 ↔ Row 3
3a-t = 0
5b-1.333t = 0
b-0.667t = -300

Row 3 - 1/5 · Row 2 → Row 3
3a-t = 0
5b-1.333t = 0
-0.4t = -300

t = -300/-0.4 = 750
b = 0+1.3333333333333t/5 = 0+1.33333333 · 750/5 = 200
a = 0+t/3 = 0+750/3 = 250

a = 250
b = 200
t = 750

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