To determine how many bottles the machine can fill in eight hours, we first need to find the rate at which the machine fills bottles.
The machine fills 5400 bottles in 3 hours. To find the number of bottles filled per hour, we divide the total number of bottles by the number of hours:
\[ \text{Bottles per hour} = \frac{5400 \text{ bottles}}{3 \text{ hours}} = 1800 \text{ bottles per hour} \]
Next, we calculate how many bottles can be filled in 8 hours by multiplying the hourly rate by the number of hours:
\[ \text{Bottles in 8 hours} = 1800 \text{ bottles per hour} \times 8 \text{ hours} = 14400 \text{ bottles} \]
Therefore, the machine can fill 14,400 bottles in eight hours.
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