3. The farmer has already plowed 5 hectares and $\frac{3}{8}$ of the field, and he still has to plow $\frac{2}{5}$ of the field and another 8 hectares. How many hectares does the entire field have? How much of it has already been plowed, and how much remains to be plowed?
3. The farmer has already plowed 5 hectares and $\frac{3}{8}$ of the field, and he still has to plow $\frac{2}{5}$ of the field and another 8 hectares. How many hectares does the entire field have? How much of it has already been plowed, and how much remains to be plowed?

## Solution.

If $x$ is the area of the entire field, then:

$5+\frac{3}{8} x+\frac{2}{5} x+8=x$

$5+\frac{3}{8} x+\frac{2}{5} x+8=x \quad / \cdot 40$

$200+15 x+16 x+320=40 x$

$520+31 x=40 x$

$31 x-40 x=-520$

$-9 x=-520$

$-9 x=-520 \quad /:(-9)$

$x=\frac{520}{9}=57 \frac{7}{9}$

The field has $57 \frac{7}{9}$ hectares.

(The procedure for solving the equation is worth 1 POINT, and the correct solution is worth 1 POINT.)

Already plowed is $5+\frac{3}{8} \cdot \frac{520}{9}=5+\frac{1}{1} \cdot \frac{65}{3}=5+21 \frac{2}{3}=26 \frac{2}{3}$ hectares.

1 POINT

Remaining to be plowed is $57 \frac{7}{9}-26 \frac{2}{3}=31+\frac{7}{9}-\frac{6}{9}=31 \frac{1}{9}$ hectares. $\qquad$
Note: Solutions should be graded as correct and then when the fraction is not converted to a mixed number.