Afternoon 5922

Tractors plowed a field of 15 3/4 ha. It plowed 3 1/3 ha in the morning, 2 5/6 ha in the afternoon, and 4 1/4 ha at night. How many hectares were left to plow the next day?

Correct answer:

x =  5 ¹⁄₃ = 16/3 ha

Step-by-step explanation:

$$\begin{gathered} S=15\frac{3}{4}=15+\frac{3}{4}=\frac{15\cdot 4+3}{4}=\frac{60+3}{4}=\frac{63}{4}=15.75\text{ha} \\ a=3\frac{1}{3}=3+\frac{1}{3}=\frac{3\cdot 3+1}{3}=\frac{9+1}{3}=\frac{10}{3}\doteq 3.3333\text{ha} \\ b=2\frac{5}{6}=2+\frac{5}{6}=\frac{2\cdot 6+5}{6}=\frac{12+5}{6}=\frac{17}{6}\doteq 2.8333\text{ha} \\ c=4\frac{1}{4}=4+\frac{1}{4}=\frac{4\cdot 4+1}{4}=\frac{16+1}{4}=\frac{17}{4}=4.25\text{ha} \\ A=a+b+c=\frac{10}{3}+\frac{17}{6}+\frac{17}{4}=\frac{40}{12}+\frac{34}{12}+\frac{51}{12}=\frac{40+34+51}{12}=\frac{125}{12}\doteq 10.4167\text{ha} \\ x=S-A=\frac{63}{4}-\frac{125}{12}=\frac{189}{12}-\frac{125}{12}=\frac{189-125}{12}=\frac{64}{12}=\frac{16}{3}\text{ha}=5\frac{1}{3}\text{ha}=5.3333\text{ha} \end{gathered}$$

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