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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.

Answer
36 in 1 ft/(144 in) = 0.25 ft
Each plant requires 0.25 ft.

304 plants 0.25 ft/plant = 76 ft
Area of border must be 76 ft

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) = 4b + 30b + 54 ft

Total area - area of bed = area of border
(4b + 30b + 54) - 54 = 76
4b + 30b - 76 = 0

By the quadratic formula,
b= [-30 √(30 44(-76))] / [24]
 = [-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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I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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