Together 2780

Vlasta, Zuzka, and Vierka shared the reward in the ratio of 2:8:5. Zuzka and Vierka had 160 euros together. How old was Vlasta?

Correct answer:

a =  24.6154 Eur

Step-by-step explanation:


b+c=160
8a = 2b
5b = 8c

b+c=160
8·a = 2·b
5·b = 8·c

b+c = 160
8a-2b = 0
5b-8c = 0

Pivot: Row 1 ↔ Row 2
8a-2b = 0
b+c = 160
5b-8c = 0

Pivot: Row 2 ↔ Row 3
8a-2b = 0
5b-8c = 0
b+c = 160

Row 3 - 1/5 · Row 2 → Row 3
8a-2b = 0
5b-8c = 0
2.6c = 160


c = 160/2.6 = 61.53846154
b = 0+8c/5 = 0+8 · 61.53846154/5 = 98.46153846
a = 0+2b/8 = 0+2 · 98.46153846/8 = 24.61538462

a = 320/13 ≈ 24.615385
b = 1280/13 ≈ 98.461538
c = 800/13 ≈ 61.538462

Our linear equations calculator calculates it.



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