Farmer 8

Farmer George cultivated 7/12 of his land with oranges and 1/5 of the remainder with cherries, and the remaining 40 acres he planted with cash crops. How much land did the farmer cultivate in all?

What fraction of land does she plant with cherries?

Correct answer:

x =  120 a
c =  1/12

Step-by-step explanation:

$$\begin{gathered} \frac{7}{12}\cdot x+\frac{1}{5}\cdot (x-\frac{7}{12}\cdot x)+40=x \\ 7/12\cdot x+1/5\cdot (x-7/12\cdot x)+40=x \\ 20x=2400 \\ x=\frac{2400}{20}=120=120\text{a} \\ x=120 \\ \text{ Verifying Solution: } \\ {x}_1=\frac{7}{12}\cdot x=\frac{7}{12}\cdot 120=\frac{7\cdot 120}{12}=\frac{840}{12}=70\text{a} \\ {x}_2=\frac{1}{5}\cdot (x-x_1)=\frac{1}{5}\cdot (120-70)=10\text{a} \\ {x}_3=40\text{a} \\ X=x_1+x_2+x_3=70+10+40=120\text{a} \\ X=x \end{gathered}$$

$c=\frac{x_2}{x}=\frac{10}{120}=\frac{1}{12}=0.0833$

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