# Procedure 34191

Petr got a fifth more than Pavel, Jirka 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.

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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