Garden Plot

ahurt879

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Joined
Mar 20, 2019
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I am constructing a garden. My plan is to place alternating rows of existing grass and planting rows within the garden plot. The plot is a 35.5x35.5 square. The grass row width is fixed 21 inches. The planting rows will be covered with 4 inches of compost. Compost costs $2.98 a bag and contains 1.5 cu feet of compost per bag. What is the min cost of compost? (The planting row width is variable)
 
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I would find the total area of the grass, subtract that from the total area of the plot, which would give the area to be covered by compost. The volume of compost is that multiplied by the depth. There are a couple conversions to do. (I assume 35.5x35.5 means feet.)
 
"35..5x35.5" what? Since you give the width of the grass strips in inches, I guess imperial units but probably not "35..5x35.5" inches! I will guess "35.5x35.5" feet. The width is 35.5 feet= 426 inches. Let the width of the planting row be "x" inches. I will also guess that the row on each side is a planting row. in order to distinguish where the garden ends and the lawn starts. That is, there is a 426- x width to be divided into an integer number of strips of width 21+ x inches: we require that $\frac{426- x}{21+ x}= n$ for some integer n. At this point I would use a little "guess and check" and find that, for x= 11 inches, n= 12.97, close enough to 13 that the last strip being just a little less that 11 inches would be unnoticeable.
 
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