Harvest 83600

Martin brought twice as much harvest as Tomáš and Filip, 15 kg more than Martin. They got a total of 65 kg of harvest. How much did each person bring?

Final Answer:

m =  20 kg
f =  35 kg
t =  10 kg

Step-by-step explanation:

$$\begin{gathered} m=2t \\ f=15+m \\ m+f+t=65 \\ m=2\cdot t \\ m-2t=0 \\ f-m=15 \\ f+m+t=65 \\ Pivot:Row1\leftrightarrow Row2 \\ Row3-Row1\to Row3 \\ 2m+t=50 \\ Pivot:Row2\leftrightarrow Row3 \\ Row3-\frac{1}{2}\cdot Row2\to Row3 \\ -2.5t=-25 \\ t=\frac{-25}{-2.5}=10 \\ m=\frac{50-t}{2}=\frac{50-10}{2}=20 \\ f=15+m=15+20=35 \\ f=35 \\ m=20 \\ t=10 \end{gathered}$$

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