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A rectangular space (6 by 9 feet) is filled with plants of one variety. 304 plants of another variety are used for a uniform border around the first variety. Planting directions for the second variety require 36 square inches for each plant.

Determine width of border. Thank you.

36 in² × 1 ft²/(144 in²) = 0.25 ft²

Each plant requires 0.25 ft².

304 plants × 0.25 ft²/plant = 76 ft²

Area of border must be 76 ft²

If the border is b ft wide, dimensions of bed plus border are is (6+2b) ft by (9+2b) ft.

Total area = (6+2b)(9+2b) = 4b² + 30b + 54 ft²

Total area - area of bed = area of border

(4b² + 30b + 54) - 54 = 76

4b² + 30b - 76 = 0

By the quadratic formula,

b = [-30 ± √(30² – 4·4(-76))] / [2·4]

= [-30 ± √2116] / 8

= [-30 ± 46] /8

= -9.5, 2

-9.5 is an extraneous solution, so b = 2 ft.

The border is 2 feet wide.

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