# According 22563

Three workers received a reward of CZK 12,600 for their joint work. They divided the money according to the work done. The first received 20% less than the second, and the third received 50% more than the first. How much did each of them get?

a =  3360
b =  4200
c =  5040

### Step-by-step explanation:

a+b+c=12600
a = b-0.20b
c = a+0.50a

a+b+c=12600
a = b-0.20·b
c = a+0.50·a

a+b+c = 12600
a-0.8b = 0
1.5a-c = 0

Pivot: Row 1 ↔ Row 3
1.5a-c = 0
a-0.8b = 0
a+b+c = 12600

Row 2 - 1/1.5 · Row 1 → Row 2
1.5a-c = 0
-0.8b+0.667c = 0
a+b+c = 12600

Row 3 - 1/1.5 · Row 1 → Row 3
1.5a-c = 0
-0.8b+0.667c = 0
b+1.667c = 12600

Pivot: Row 2 ↔ Row 3
1.5a-c = 0
b+1.667c = 12600
-0.8b+0.667c = 0

Row 3 - -0.8 · Row 2 → Row 3
1.5a-c = 0
b+1.667c = 12600
2c = 10080

c = 10080/2 = 5040
b = 12600-1.6666666666667c = 12600-1.66666667 · 5040 = 4200
a = 0+c/1.5 = 0+5040/1.5 = 3360

a = 3360
b = 4200
c = 5040

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