Complaining 9611

Ondra, Mathias, and Kuba are returning from collecting nuts. They have a total of 120. Mathias complains that Ondra has the most, as always. The father orders Ondra to sprinkle it on his Mathias so that the number of nuts doubles. Now Cuba is complaining that he has the most.
At his father's command, Mathias sprinkles Kuba with double the number of nuts. Ondra is angry that he has the fewest now, so Cuba sprinkles Ondra with double the number of nuts. Now everyone has the same, and finally, they are calm.

How many nuts did each of the boys initially have?

Correct answer:

o =  55
m =  35
k =  30

Step-by-step explanation:

o+m+k = 120  o1​ = o−m m1​ = m+m = 2m k1​ = k  m2​ = m1​−k1​ = 2m−k k2​ = k1​ + k1​ = 2k1​ = 2k o2​ = o1​  o3​ = o2​ + o2​ = o1​ + o1​ = (o−m)+(o−m) k3​ = k2​ − o2​ = 2k − o1​ = 2k − (o−m) m3​ = m2​  o+m+k=120 2k−(o−m)=120/3 (o−m)+(o−m)=120/3  o+m+k=120 2⋅ k−(o−m)=120/3 (o−m)+(o−m)=120/3  k+m+o=120 6k+3m−3o=120 6m−6o=−120  Pivot:Row1↔Row2 6k+3m−3o=120 k+m+o=120 6m−6o=−120  Row2−61​⋅ Row1→Row2 6k+3m−3o=120 0.5m+1.5o=100 6m−6o=−120  Pivot:Row2↔Row3 6k+3m−3o=120 6m−6o=−120 0.5m+1.5o=100  Row3−60.5​⋅ Row2→Row3 6k+3m−3o=120 6m−6o=−120 2o=110  o=2110​=55 m=6−120+6o​=6−120+6⋅ 55​=35 k=6120−3m+3o​=6120−3⋅ 35+3⋅ 55​=30  k=30 m=35 o=55
m=35
k=30  skuska/zkouska: o1​=o−m=55−35=20 m1​=m+m=35+35=70 k1​=k=30  o2​=o1​=20 m2​=m1​−k1​=70−30=40 k2​=k1​+k1​=30+30=60  o3​=o2​+o2​=20+20=40 m3​=m2​=40 k3​=k2​−o2​=60−20=40

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