To determine how many 4-pound bags of lawn seed are needed to cover 8400 square feet, we first need to establish the coverage provided by one 4-pound bag of lawn seed.
From the problem, we know that 3 pounds of lawn seed covers 1800 square feet. Therefore, we can find how much area 1 pound of lawn seed covers:
\[ \text{Area covered by 1 pound} = \frac{1800 \text{ square feet}}{3 \text{ pounds}} = 600 \text{ square feet per pound} \]
Next, we find out how much area one 4-pound bag covers:
\[ \text{Area covered by a 4-pound bag} = 4 \text{ pounds} \times 600 \text{ square feet per pound} = 2400 \text{ square feet} \]
Now we will calculate how many 4-pound bags are needed to cover 8400 square feet:
\[ \text{Number of 4-pound bags needed} = \frac{8400 \text{ square feet}}{2400 \text{ square feet per bag}} = 3.5 \]
Since we cannot purchase a fraction of a bag, we must round up to the nearest whole number. Therefore, we need:
\[ \text{Number of bags needed} = 4 \]
Thus, to cover 8400 square feet, 4 four-pound bags of lawn seed are needed.
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