Orač je već izorao 5 5 5 3 8 \frac38 8 3 2 5 \frac25 5 2 8 8 8
Rješenje Ako je x x x
5 + 3 8 x + 2 5 x + 8 = x . 5+\frac38x+\frac25x+8=x. 5 + 8 3 x + 5 2 x + 8 = x . Rješavamo jednadžbu:
5 + 3 8 x + 2 5 x + 8 = x / ⋅ 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 9 = 57 7 9 . \begin{aligned} 5+\frac38x+\frac25x+8&=x &&/\cdot40\\ 200+15x+16x+320&=40x\\ 520+31x&=40x\\ 31x-40x&=-520\\ -9x&=-520 &&/: (-9)\\ x&=\frac{520}{9}=57\frac79. \end{aligned} 5 + 8 3 x + 5 2 x + 8 200 + 15 x + 16 x + 320 520 + 31 x 31 x − 40 x − 9 x x = x = 40 x = 40 x = − 520 = − 520 = 9 520 = 57 9 7 . / ⋅ 40 / : ( − 9 ) Oranica ima 57 7 9 57\frac79 57 9 7
Preorano je
5 + 3 8 ⋅ 520 9 = 5 + 1 1 ⋅ 65 3 = 5 + 21 2 3 = 26 2 3 5+\frac38\cdot\frac{520}{9} =5+\frac11\cdot\frac{65}{3} =5+21\frac23 =26\frac23 5 + 8 3 ⋅ 9 520 = 5 + 1 1 ⋅ 3 65 = 5 + 21 3 2 = 26 3 2 hektara.
Za orati preostaje
57 7 9 − 26 2 3 = 31 + 7 9 − 6 9 = 31 1 9 57\frac79-26\frac23 =31+\frac79-\frac69 =31\frac19 57 9 7 − 26 3 2 = 31 + 9 7 − 9 6 = 31 9 1 hektara.
