Three 222

Three tractor drivers working on a private farm together played 24 hectares of land in a shift. The first drive played half the second, and the second 4 hectares more than the third. Calculate the number of hectares played by the first, second and third.

Correct answer:

a =  5.6 ha
b =  11.2 ha
c =  7.2 ha

Step-by-step explanation:

$$\begin{gathered} a+b+c=24 \\ a=b/2 \\ b=4+c \\ a+b+c=24 \\ 2a-b=0 \\ b-c=4 \\ Pivot:Row1\leftrightarrow Row2 \\ 2a-b=0 \\ a+b+c=24 \\ b-c=4 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a-b=0 \\ 1.5b+c=24 \\ b-c=4 \\ Row3-\frac{1}{1.5}\cdot Row2\to Row3 \\ 2a-b=0 \\ 1.5b+c=24 \\ -1.667c=-12 \\ c=\frac{-12}{-1.66666667}=7.2 \\ b=\frac{24-c}{1.5}=\frac{24-7.2}{1.5}=11.2 \\ a=\frac{0+b}{2}=\frac{0+11.2}{2}=5.6 \\ a=\frac{28}{5}=5.6 \\ b=\frac{56}{5}=11.2 \\ c=\frac{36}{5}=7.2 \end{gathered}$$

Try another example