First, let's convert the capacity of the dump truck from tons to pounds so we can work with consistent units.
Since 1 ton equals 2000 pounds, we can convert 2 1/4 tons as follows:
\[ 2 \frac{1}{4} \text{ tons} = 2.25 \text{ tons} = 2.25 \times 2000 \text{ pounds} = 4500 \text{ pounds} \]
Next, we know that the pay loader puts 750 pounds of gravel into the truck at one time.
To find the number of loads needed to fill the truck, we can divide the truck's total capacity (in pounds) by the amount of gravel dumped each time (also in pounds):
\[ \frac{4500 \text{ pounds}}{750 \text{ pounds/load}} = 6 \text{ loads} \]
Thus, the pay loader needs to dump 6 loads of gravel into the truck before it is full.
The correct answer is 6 loads.
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