Reward distribution

Petr got a fifth more than Pavel, George got 100 CZK more than Petr, and Honza got half of what Petr did, so they shared the reward of CZK 2,500. Solution and procedure.

Final Answer:

a =  600
h =  360
j =  820
p =  720

Step-by-step explanation:


p+j+a+h=2500
p = a + a/5
j= 100+ p
h = p/2

a+h+j+p = 2500
6a-5p = 0
j-p = 100
2h-p = 0

Pivot: Row 1 ↔ Row 2
6a-5p = 0
a+h+j+p = 2500
j-p = 100
2h-p = 0

Row 2 - 1/6 · Row 1 → Row 2
6a-5p = 0
h+j+1.8333p = 2500
j-p = 100
2h-p = 0

Pivot: Row 2 ↔ Row 4
6a-5p = 0
2h-p = 0
j-p = 100
h+j+1.8333p = 2500

Row 4 - 1/2 · Row 2 → Row 4
6a-5p = 0
2h-p = 0
j-p = 100
j+2.3333p = 2500

Row 4 - Row 3 → Row 4
6a-5p = 0
2h-p = 0
j-p = 100
3.3333p = 2400


p = 2400/3.33333333 = 720
j = 100+p = 100+720 = 820
h = 0+p/2 = 0+720/2 = 360
a = 0+5p/6 = 0+5 · 720/6 = 600

a = 600
h = 360
j = 820
p = 720

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