story problem

Question

A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $2.50 per foot and the cost of preparing the soil is $1.00 per ft2, determine the size of the garden that can be enclosed for $504.00.

Answer 1

Ali,

Write equations to represent the relationships in the problem.

 

Let x be the side length of the square garden,

the perimeter is given by 4x and the area is x².

 

The cost to fence the garden will be (4x)(2.50) and the cost to prepare the soil is ($1)(x²)

 

504 = (4x)(2.50) + (1)(x²)   This is a quadratic equation. Solve.

 

504= 10x + x²

 

x²  + 10x -504 =0

 

(x+28)(x -18) = 0

 

The length has to be a positive quantity, therefore,

 

x = 18

 

Check

 

504 =  (4)(18)(2.50)  +  (18² )

 

504  =  180  +  324      It is correct.

 

 

The side length of the vegetable garden is 18 feet, the perimeter is 4(18) = 72 feet and the area is (18²) = 324 sq. feet.