# Remuneration

Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and the third 4000 CZK less than a second employee. How many CZK does each receive?

a =  15000
b =  18000
c =  14000

### Step-by-step explanation:

a+b+c=47000
b = 1.20 a
c = b - 4000

a+b+c=47000
b = 1.20·a
c = b - 4000

a+b+c = 47000
1.2a-b = 0
b-c = 4000

Pivot: Row 1 ↔ Row 2
1.2a-b = 0
a+b+c = 47000
b-c = 4000

Row 2 - 1/1.2 · Row 1 → Row 2
1.2a-b = 0
1.833b+c = 47000
b-c = 4000

Row 3 - 1/1.83333333 · Row 2 → Row 3
1.2a-b = 0
1.833b+c = 47000
-1.545c = -21636.364

c = -21636.36363636/-1.54545455 = 14000
b = 47000-c/1.83333333 = 47000-14000/1.83333333 = 18000
a = 0+b/1.2 = 0+18000/1.2 = 15000

a = 15000
b = 18000
c = 14000

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