A rectangular garden of area 50 square feet is to be surrounded on three sides by a fence costing $2 per running foot and on one side by a brick wall costing $6 per running foot. Let x be the length of the brick wall side. Which of the following represents the total cost of the material?
A) 3x + (50 - x)
B) 6x + $\frac { 50 } { x }$
C) 6x + $\frac { 300 } { x }$
D) $\frac { 3 x } { 50 }+ \frac { 1 } { 50 x }$
E) none of these

Question

Quizplus · Accepted Answer

The area of the garden is given as 50 square feet, with one side (length x) being a brick wall and the other three sides being fenced. The cost of the brick wall is $6 per running foot, and the cost of the fence is $2 per running foot. The total cost of the material can be calculated by first finding the perimeter of the rectangle, then calculating the cost of the brick wall and the fence separately.Given the area $A = 50$ and one side $x$, the other side can be represented as $\frac{50}{x}$ because $A = x \times \text{(other side)}$. The total length of the fencing required is the sum of the two sides and one x side, which is $2 \times \frac{50}{x} + x$. The cost of the fencing is then $2 \times (2 \times \frac{50}{x} + x) = 4 \times \frac{50}{x} + 2x$. The cost of the brick wall is $6x$.Therefore, the total cost is the sum of the cost of the fencing and the brick wall, which is $6x + 4 \times \frac{50}{x} + 2x$. However, none of the provided options correctly represents this calculation, leading to the conclusion that the correct answer is "none of these."

A Rectangular Garden of Area 50 Square Feet Is to Be