Polovicu 3791

X + Y = 31835
X je množstvo, ktoré nakradli 1,2 a 3
Y je množstvo, ktoré nakradli 4 a 5
1. ukradol polovicu X,
2 . polovicu zvyšku a ešte 3 k tomu
3. ukradol 6801,5
4. Ukradol 1/9 z Y, čo je 513
5. Nakradol zvyšok

Správna odpoveď:

X = 27206
Y = 4629
a = 13603
b = 6801,5
c = 6801,5
d = 513
f = 4116

Postup správneho riešenia:

X + Y = 31835
X = a+b+c
Y = d + f
a=X/2
b = (X-a)/2
c = 6801,5
d = 513

X+Y = 31835
X-a-b-c = 0
Y-d-f = 0
X-2a = 0
X-a-2b = 0
c = 6801,5
d = 513

Riadok 2 - Riadok 1 → Riadok 2
X+Y = 31835
-Y-a-b-c = -31835
Y-d-f = 0
X-2a = 0
X-a-2b = 0
c = 6801,5
d = 513

Riadok 4 - Riadok 1 → Riadok 4
X+Y = 31835
-Y-a-b-c = -31835
Y-d-f = 0
-Y-2a = -31835
X-a-2b = 0
c = 6801,5
d = 513

Riadok 5 - Riadok 1 → Riadok 5
X+Y = 31835
-Y-a-b-c = -31835
Y-d-f = 0
-Y-2a = -31835
-Y-a-2b = -31835
c = 6801,5
d = 513

Riadok 3 + Riadok 2 → Riadok 3
X+Y = 31835
-Y-a-b-c = -31835
-a-b-c-d-f = -31835
-Y-2a = -31835
-Y-a-2b = -31835
c = 6801,5
d = 513

Riadok 4 - Riadok 2 → Riadok 4
X+Y = 31835
-Y-a-b-c = -31835
-a-b-c-d-f = -31835
-a+b+c = 0
-Y-a-2b = -31835
c = 6801,5
d = 513

Riadok 5 - Riadok 2 → Riadok 5
X+Y = 31835
-Y-a-b-c = -31835
-a-b-c-d-f = -31835
-a+b+c = 0
-b+c = 0
c = 6801,5
d = 513

Riadok 4 - Riadok 3 → Riadok 4
X+Y = 31835
-Y-a-b-c = -31835
-a-b-c-d-f = -31835
2b+2c+d+f = 31835
-b+c = 0
c = 6801,5
d = 513

Riadok 5 - -1/2 · Riadok 4 → Riadok 5
X+Y = 31835
-Y-a-b-c = -31835
-a-b-c-d-f = -31835
2b+2c+d+f = 31835
2c+0,5d+0,5f = 15917,5
c = 6801,5
d = 513

Riadok 6 - 1/2 · Riadok 5 → Riadok 6
X+Y = 31835
-Y-a-b-c = -31835
-a-b-c-d-f = -31835
2b+2c+d+f = 31835
2c+0,5d+0,5f = 15917,5
-0,25d-0,25f = -1157,25
d = 513

Pivot: Riadok 6 ↔ Riadok 7
X+Y = 31835
-Y-a-b-c = -31835
-a-b-c-d-f = -31835
2b+2c+d+f = 31835
2c+0,5d+0,5f = 15917,5
d = 513
-0,25d-0,25f = -1157,25

Riadok 7 - -0,25 · Riadok 6 → Riadok 7
X+Y = 31835
-Y-a-b-c = -31835
-a-b-c-d-f = -31835
2b+2c+d+f = 31835
2c+0,5d+0,5f = 15917,5
d = 513
-0,25f = -1029

f = -1029/-0,25 = 4116
d = 513/1 = 513
c = 15917,5-0,5d-0,5f/2 = 15917,5-0,5 · 513-0,5 · 4116/2 = 6801,5
b = 31835-2c-d-f/2 = 31835-2 · 6801,5-513-4116/2 = 6801,5
a = -31835+b+c+d+f/-1 = -31835+6801,5+6801,5+513+4116/-1 = 13603
Y = -31835+a+b+c/-1 = -31835+13603+6801,5+6801,5/-1 = 4629
X = 31835-Y = 31835-4629 = 27206

X = 27206
Y = 4629
a = 13603
b = 13603/2 = 6801,5
c = 13603/2 = 6801,5
d = 513
f = 4116

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