The area, in acres, used to plant the green apples is
[tex]7\frac{1}{5}=7+\frac{1}{5}=\frac{5\cdot7+1}{5}=\frac{35+1}{5}=\frac{36}{5}[/tex]
And this area corresponds to 3/8 of the entire orchard.
So, calling x the area of the entire orchard, we have the following proportion:
Area in acres Fraction of the orchard
36/5 3/8
x 1
Then, cross multiplying the above values, we obtain:
[tex]\begin{gathered} \frac{3}{8}x=\frac{36}{5} \\ \\ \frac{8}{3}\cdot\frac{3}{8}x=\frac{8}{3}\cdot\frac{36}{5} \\ \\ x=\frac{8}{5}\cdot\frac{36}{3} \\ \\ x=\frac{8}{5}\cdot12 \\ \\ x=\frac{96}{5} \\ \\ x=\frac{95}{5}+\frac{1}{5} \\ \\ x=19\frac{1}{5} \end{gathered}[/tex]
Therefore, the area of the framer's orchard is 19 1/5 acres.
