# Performances 2459

Three part-timers received a total of 2,800 Euros for their work. They divided them according to their performances so that the first got 2/5 less than the second and the third got 50 Euros more than the first. How many crowns did the third one get?

c =  800

## Step-by-step explanation:

a+b+c=2800
a = b - 2/5 b
c = a+50

a+b+c=2800
a = b - 2/5·b
c = a+50

a+b+c = 2800
5a-3b = 0
a-c = -50

Pivot: Row 1 ↔ Row 2
5a-3b = 0
a+b+c = 2800
a-c = -50

Row 2 - 1/5 · Row 1 → Row 2
5a-3b = 0
1.6b+c = 2800
a-c = -50

Row 3 - 1/5 · Row 1 → Row 3
5a-3b = 0
1.6b+c = 2800
0.6b-c = -50

Row 3 - 0.6/1.6 · Row 2 → Row 3
5a-3b = 0
1.6b+c = 2800
-1.375c = -1100

c = -1100/-1.375 = 800
b = 2800-c/1.6 = 2800-800/1.6 = 1250
a = 0+3b/5 = 0+3 · 1250/5 = 750

a = 750
b = 1250
c = 800

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