Pasture 79214

I need to find out the number of bulls in the third period. In the first period, 12 bulls grazed on 3 and 1/3 ha for 4 weeks. In the second period, 21 bulls graze on 10 ha for 9 weeks. How many bulls in the third period graze for 24ha and 18 weeks? The pasture grows evenly.

Correct answer:

c = 36

Step-by-step explanation:

a = 12 S_{1} = 3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{3 \cdot 3 + 1}{3} = \frac{9 + 1}{3} = \frac{1 0}{3} = 3 \frac{1}{3} ≐ 3.3333 ha t_{1} = 4 b = 21 S_{2} = 10 ha t_{2} = 9 S_{3} = 24 ha t_{3} = 18 S_{1} - a \cdot X \cdot t_{1} + S_{1} \cdot t_{1} \cdot Y = 0 S_{2} - b \cdot X \cdot t_{2} + S_{2} \cdot t_{2} \cdot Y = 0 3.3333333333333 - 12 \cdot X \cdot 4 + 3.3333333333333 \cdot 4 \cdot Y = 0 10 - 21 \cdot X \cdot 9 + 10 \cdot 9 \cdot Y = 0 48 X - 13.333333 Y = 3.333333 189 X - 90 Y = 10 P i v o t : R o w 1 \leftrightarrow R o w 2 189 X - 90 Y = 10 48 X - 13.33 Y = 3.33 R o w 2 - \frac{4 8}{1 8 9} \cdot R o w 1 \to R o w 2 189 X - 90 Y = 10 9.52 Y = 0.79 Y = \frac{0 . 7 9 3 6 5 0 7 9}{9 . 5 2 3 8 0 9 5 2} = 0.08333333 X = \frac{1 0 + 9 0 Y}{1 8 9} = \frac{1 0 + 9 0 \cdot 0 . 0 8 3 3 3 3 3 3}{1 8 9} = 0.09259259 X = \frac{5}{5 4} ≐ 0.092593 Y = \frac{1}{1 2} ≐ 0.083333 S_{3} - c \cdot X \cdot t_{3} + S_{3} \cdot t_{3} \cdot Y = 0 24 - c \cdot 0.09259259259259 \cdot 18 + 24 \cdot 18 \cdot 0.083333333333329 = 0 1.666667 c = 60 c = \frac{6 0}{1 . 6 6 6 6 6 6 6 7} = 36 c = 36

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