Bonus sequence

The bonuses were paid to four people in sequence, with each subsequent person receiving double what the previous person received. How many crowns in premiums did each person receive, if a total of 2625 CZK was paid for all premiums?

Final Answer:

a =  175
b =  350
c =  700
d =  1400

Step-by-step explanation:


a+b+c+d=2625
b= 2a
c = 2b
d = 2c

a+b+c+d=2625
b= 2·a
c = 2·b
d = 2·c

a+b+c+d = 2625
2a-b = 0
2b-c = 0
2c-d = 0

Pivot: Row 1 ↔ Row 2
2a-b = 0
a+b+c+d = 2625
2b-c = 0
2c-d = 0

Row 2 - 1/2 · Row 1 → Row 2
2a-b = 0
1.5b+c+d = 2625
2b-c = 0
2c-d = 0

Pivot: Row 2 ↔ Row 3
2a-b = 0
2b-c = 0
1.5b+c+d = 2625
2c-d = 0

Row 3 - 1.5/2 · Row 2 → Row 3
2a-b = 0
2b-c = 0
1.75c+d = 2625
2c-d = 0

Pivot: Row 3 ↔ Row 4
2a-b = 0
2b-c = 0
2c-d = 0
1.75c+d = 2625

Row 4 - 1.75/2 · Row 3 → Row 4
2a-b = 0
2b-c = 0
2c-d = 0
1.875d = 2625


d = 2625/1.875 = 1400
c = 0+d/2 = 0+1400/2 = 700
b = 0+c/2 = 0+700/2 = 350
a = 0+b/2 = 0+350/2 = 175

a = 175
b = 350
c = 700
d = 1400

Our linear equations calculator calculates it.



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