Dividing money

Thomas, Honza and Vasek are to divide 1220kč. Honza got 25% more than Thomas. Vasek is 20% less than Thomas. How many CZK does each get?

Correct answer:

a =  400
b =  500
c =  320

Step-by-step explanation:


a+b+c=1220
b = a+0.25a
c = a-0.20a

a+b+c=1220
b = a+0.25·a
c = a-0.20·a

a+b+c = 1220
1.25a-b = 0
0.8a-c = 0

Pivot: Row 1 ↔ Row 2
1.25a-b = 0
a+b+c = 1220
0.8a-c = 0

Row 2 - 1/1.25 · Row 1 → Row 2
1.25a-b = 0
1.8b+c = 1220
0.8a-c = 0

Row 3 - 0.8/1.25 · Row 1 → Row 3
1.25a-b = 0
1.8b+c = 1220
0.64b-c = 0

Row 3 - 0.64/1.8 · Row 2 → Row 3
1.25a-b = 0
1.8b+c = 1220
-1.356c = -433.778


c = -433.77777778/-1.35555556 = 320
b = 1220-c/1.8 = 1220-320/1.8 = 500
a = 0+b/1.25 = 0+500/1.25 = 400

a = 400
b = 500
c = 320

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