Contestants

The three best contestants are to divide the total prize of CZK 4,200. The second gets 20% more than the third. And the first one gets 200 CZK less than the second and the third together. How much will everyone get?

Correct answer:

a =  2000
b =  1200
c =  1000

Step-by-step explanation:


a+b+c= 4200
b = c+0.20c
a = (b+c)-200

a+b+c= 4200
b = c+0.20·c
a = (b+c)-200

a+b+c = 4200
b-1.2c = 0
a-b-c = -200

Row 3 - Row 1 → Row 3
a+b+c = 4200
b-1.2c = 0
-2b-2c = -4400

Pivot: Row 2 ↔ Row 3
a+b+c = 4200
-2b-2c = -4400
b-1.2c = 0

Row 3 - 1/-2 · Row 2 → Row 3
a+b+c = 4200
-2b-2c = -4400
-2.2c = -2200


c = -2200/-2.2 = 1000
b = -4400+2c/-2 = -4400+2 · 1000/-2 = 1200
a = 4200-b-c = 4200-1200-1000 = 2000

a = 2000
b = 1200
c = 1000

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