SOLUTION: A rectangular piece of land to be developed as a memorial park has an area of 48 m^2. The length of the lot is three times the width of the lot. A rectangular path whose width is x

Question 805748: A rectangular piece of land to be developed as a memorial park has an area of 48 m^2. The length of the lot is three times the width of the lot. A rectangular path whose width is x meters is to be constructed along the inner perimeter of the lot. The land contained within the path will be landscaped. The cost to construct the path is $2 per square meter and the cost to landscape the inner field is $3 per square meter. Express the total cost to develop this lot as a function of x, the width of the path.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
the area of plot = 48 m^2
ratio is 1/3
Width = 1/4 * 48 = 12m
length = 3times 12 = 36m
the width is x
Inner garden length = 36-2x
inner garden width = 12-2x
Area of garden = (36-2x)(12-2x)
Land scaping the garden $3 / m^2
Cost of landscaping = 3(36-2x)(12-2x)
Cost of pavement
area of pavement = total area - area of inner garden
48- 3(36-2x)(12-2x)
cost of pavement = $2 /m^2
Cost of pavement = 2(48-3(36-2x)(12-2x))
Total cost
total cost C= cost of pavement + cost of landscaping inner garden
C= 2(48-3(36-2x)(12-2x)) + 3(36-2x)(12-2x)
= 96-6(36-2x)(12-2x)) + 3(36-2x)(12-2x)
simplify if necessary

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