SOLUTION: A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $4.00 per foot and the cost of preparing the soil is $0.80 per ft^2, determine the size

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Question 901507: A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $4.00 per foot and the cost of preparing the soil is $0.80 per ft^2, determine the size of the garden that can be enclosed for $640.00.
________ ft^2
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the side length of the square garden.

Perimeter is 4x.
Area is x%5E2.

Fence cost, 4x%2A4=16x dollars
Soil preparation cost, %28x%5E2%29%280.80%29 dollars

Total cost wanted is $640;
0.8x%5E2%2B16x=640

Possible simplification:
highlight%28x%5E2%2B20x-800=0%29
Using this equation, first find discriminant:
20%5E2%2B4%2A800=400%2B3200=3600=%286%2A10%29%5E2=60%5E2.
Discriminant is 60%5E2.

x=%28-20%2Bsqrt%2860%5E2%29%29%2F2
x=%28-20%2B60%29%2F2
highlight%28x=20%29
(The quadratic equation is factorable, and that could be done if desired).

ANSWER CONCLUSION: Garden side length, 20 feet, and area 400 square feet.