Three friends

Divide 570 euros among three friends so that first will get 50 euros less than the second and the third twice more than the first. How many euros will get everyone?

Correct answer:

a =  130
b =  180
c =  260

Step-by-step explanation:


570 = a+b+c
a = b-50
c = 2a

570 = a+b+c
a = b-50
c = 2·a

a+b+c = 570
a-b = -50
2a-c = 0

Pivot: Row 1 ↔ Row 3
2a-c = 0
a-b = -50
a+b+c = 570

Row 2 - 1/2 · Row 1 → Row 2
2a-c = 0
-b+0.5c = -50
a+b+c = 570

Row 3 - 1/2 · Row 1 → Row 3
2a-c = 0
-b+0.5c = -50
b+1.5c = 570

Row 3 + Row 2 → Row 3
2a-c = 0
-b+0.5c = -50
2c = 520


c = 520/2 = 260
b = -50-0.5c/-1 = -50-0.5 · 260/-1 = 180
a = 0+c/2 = 0+260/2 = 130

a = 130
b = 180
c = 260

Our linear equations calculator calculates it.



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