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Quadratic Equation Word Problem

Sasha works at the Botanical Gardens and is planning a new rectangular Rose Garden 20 meters by 30 meters she plans to build walkway with a uniform width all around the garden. Her budget is $6,000 and she knows it will cost $10 per meter squared to construct a walkway. How wide can the walkway be?

Respuesta :

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Define x :
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Let the width be x.

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Find Area of the walkway :
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Area = 30x + 30x + 20x + 20x + 4x²       
Area = 100x + 4x²

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Find cost of the walkway in term of x:
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1m² = $10
100x + 4x² = 10(4x² + 100x)
(100x + 4x²)m = $(40x² + 1000x)

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Find Width of the walkway :
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The budget is $6000

40x² + 1000x = 6000
40x² + 1000x - 6000 = 0
x² + 25x -150 = 0              //Divide by 40 through
(x - 5)(x + 30) = 0             //Factorise
x = 5 or x = -30 (Rejected, width cannot be negative)

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Answer: The width can be 5m wide.
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