# Warehouse 15843

They sold coal in a coal warehouse for three days. On the first day, they sold a quarter of the coal, 2/3 of the rest on the second day, and the remaining 300 tons of coal on the third day. How many tons of coal did they sell the next day?

b =  600 t

## Step-by-step explanation:

a+b+300 = t
a = t/4
b = 2/3·(t-a)

a+b-t = -300
4a-t = 0
2a+3b-2t = 0

Pivot: Row 1 ↔ Row 2
4a-t = 0
a+b-t = -300
2a+3b-2t = 0

Row 2 - 1/4 · Row 1 → Row 2
4a-t = 0
b-0.75t = -300
2a+3b-2t = 0

Row 3 - 2/4 · Row 1 → Row 3
4a-t = 0
b-0.75t = -300
3b-1.5t = 0

Pivot: Row 2 ↔ Row 3
4a-t = 0
3b-1.5t = 0
b-0.75t = -300

Row 3 - 1/3 · Row 2 → Row 3
4a-t = 0
3b-1.5t = 0
-0.25t = -300

t = -300/-0.25 = 1200
b = 0+1.5t/3 = 0+1.5 · 1200/3 = 600
a = 0+t/4 = 0+1200/4 = 300

a = 300
b = 600
t = 1200

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