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Question
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

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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#### Janet Yang

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