Question

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?

Answer 1

------------------------------------------------------
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.
------------------------------------------------------