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?
------------------------------------------------------ Define x : ------------------------------------------------------ Let the width be x.
------------------------------------------------------ Find Area of the walkway : ------------------------------------------------------ Area = 30x + 30x + 20x + 20x + 4x² Area = 100x + 4x²
------------------------------------------------------ Find cost of the walkway in term of x: ------------------------------------------------------ 1m² = $10 100x + 4x² = 10(4x² + 100x) (100x + 4x²)m = $(40x² + 1000x)
------------------------------------------------------ Find Width of the walkway : ------------------------------------------------------ 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)
------------------------------------------------------ Answer: The width can be 5m wide. ------------------------------------------------------
