Three friends

The three friends spent 600 KC in a teahouse. Thomas paid twice as much as Paul. Paul was half less than Zdeněk. How many each paid?

Correct answer:

T =  240 Kc
P =  120 Kc
Z =  240 Kc

Step-by-step explanation:


T+P+Z = 600
T = 2·P
P = Z/2

P+T+Z = 600
2P-T = 0
2P-Z = 0

Pivot: Row 1 ↔ Row 2
2P-T = 0
P+T+Z = 600
2P-Z = 0

Row 2 - 1/2 · Row 1 → Row 2
2P-T = 0
1.5T+Z = 600
2P-Z = 0

Row 3 - Row 1 → Row 3
2P-T = 0
1.5T+Z = 600
T-Z = 0

Row 3 - 1/1.5 · Row 2 → Row 3
2P-T = 0
1.5T+Z = 600
-1.667Z = -400


Z = -400/-1.66666667 = 240
T = 600-Z/1.5 = 600-240/1.5 = 240
P = 0+T/2 = 0+240/2 = 120

P = 120
T = 240
Z = 240

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