Donuts

In the dining room, Thomas, Philip, and Martin sit at one table. Together, they eat 36 doughnuts. Philip ate twice as much as Thomas, and Martin ate half more than Philip. How many doughnuts did each eat?

Final 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

Our linear equations calculator calculates it.



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