Donuts

At one table, Thomas, Filip, and Martin sit in the dining room. Together they eat 36 donuts. Filip ate twice as much as Thomas and Martin half over Filip? How many have donuts eaten each?

Correct answer:

F =  12
M =  18
T =  6

Step-by-step explanation:


T+F+M=36
F=2·T
M=F+F/2

F+M+T = 36
F-2T = 0
3F-2M = 0

Pivot: Row 1 ↔ Row 3
3F-2M = 0
F-2T = 0
F+M+T = 36

Row 2 - 1/3 · Row 1 → Row 2
3F-2M = 0
0.667M-2T = 0
F+M+T = 36

Row 3 - 1/3 · Row 1 → Row 3
3F-2M = 0
0.667M-2T = 0
1.667M+T = 36

Pivot: Row 2 ↔ Row 3
3F-2M = 0
1.667M+T = 36
0.667M-2T = 0

Row 3 - 0.66666667/1.66666667 · Row 2 → Row 3
3F-2M = 0
1.667M+T = 36
-2.4T = -14.4


T = -14.4/-2.4 = 6
M = 36-T/1.66666667 = 36-6/1.66666667 = 18
F = 0+2M/3 = 0+2 · 18/3 = 12

F = 12
M = 18
T = 6

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