A farmer 9

A farmer has 3 hectares of an orchard. ½ of the land is occupied by apples, ⅙ of the remainder is occupied by lemon trees, and tree tomatoes occupy the rest of it. Find the fraction of the land occupied by tree tomatoes.

Final Answer:

c =  5/12

Step-by-step explanation:

$$\begin{gathered} S=3\text{ha} \\ a=\frac{1}{2}=0.5 \\ b=\frac{1}{6}\cdot (1-a)=\frac{1}{6}\cdot (1-\frac{1}{2})=\frac{1}{12}\doteq 0.0833 \\ c=\frac{1}{1}-a-b=\frac{1}{1}-\frac{1}{2}-\frac{1}{12}=\frac{12}{12}-\frac{6}{12}-\frac{1}{12}=\frac{12-6-1}{12}=\frac{5}{12}\doteq 0.4167 \\ \text{ Verifying Solution: } \\ {S}_1=a\cdot S=\frac{1}{2}\cdot 3=\frac{1\cdot 3}{2}=\frac{3}{2}=1.5\text{ha} \\ {S}_2=b\cdot S=\frac{1}{12}\cdot 3=\frac{1\cdot 3}{12}=\frac{3}{12}=\frac{1}{4}=0.25\text{ha} \\ {S}_3=c\cdot S=\frac{5}{12}\cdot 3=\frac{5\cdot 3}{12}=\frac{15}{12}=\frac{5}{4}=1\frac{1}{4}=1.25\text{ha} \\ A=S_1+S_2+S_3=\frac{3}{2}+\frac{1}{4}+\frac{5}{4}=\frac{6}{4}+\frac{1}{4}+\frac{5}{4}=\frac{6+1+5}{4}=\frac{12}{4}=3 \end{gathered}$$

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