Quadratic equation word problemsasha 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)


The width can be 5m wide.

The pie is multyplued by the second step