# Performance 5041

Three workers received a reward of €2,850 for their work. They divided them according to their performance so that the first received 20% less than the second and the third received €50 more than the second. How many euros did each person receive?

a =  800
b =  1000
c =  1050

### Step-by-step explanation:

a+b+c=2850
a = b - 20/100b
c = 50+b

a+b+c=2850
a = b - 20/100·b
c = 50+b

a+b+c = 2850
100a-80b = 0
b-c = -50

Pivot: Row 1 ↔ Row 2
100a-80b = 0
a+b+c = 2850
b-c = -50

Row 2 - 1/100 · Row 1 → Row 2
100a-80b = 0
1.8b+c = 2850
b-c = -50

Row 3 - 1/1.8 · Row 2 → Row 3
100a-80b = 0
1.8b+c = 2850
-1.556c = -1633.333

c = -1633.33333333/-1.55555556 = 1050
b = 2850-c/1.8 = 2850-1050/1.8 = 1000
a = 0+80b/100 = 0+80 · 1000/100 = 800

a = 800
b = 1000
c = 1050

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