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A farmer plants 7 1/5acres of green apples in his orchard. This makes up 3/8 of his entire orchard. How many acres make up the farmer's orchard?

A Farmer Plants 7 15acres Of Green Apples In His Orchard This Makes Up 38 Of His Entire Orchard How Many Acres Make Up The Farmers Orchard class=

Sagot :

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.

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