Area as a function of side w/ relation to cost

[EIGHTSIX7]

Homework Statement

A security fence is to be built around a rectangular parking lot. The front side of the fence costs $60 per meter and the other three sides cost $30 per meter. The total cost of the fence is budgeted to be $7500.

Part a).

Express the area of the lot enclosed by the fence as a function of the length 'x' of the side that cost $60 per meter.

Homework Equations

A=length*width

The Attempt at a Solution

I have scanned and uploaded my attempt/work onto imgur. here


http://i.imgur.com/SDB9T.jpg


I have attempted the solution, where I had simplified the equation in relation to the cost I am not entirely sure if after that I had solved for the correct variable ( either y or x), and did I input the equation into the right equation (Area of rectangle as a function of length x).

Any help would be greatly appreciated. Is my attempt correct?

*****also, confused when they ask for the area of the lot as a function of the length x. So essentially I only want variable "x" in my area equation?******

 

[Dick]

Homework Statement

A security fence is to be built around a rectangular parking lot. The front side of the fence costs $60 per meter and the other three sides cost $30 per meter. The total cost of the fence is budgeted to be $7500.

Part a).

Express the area of the lot enclosed by the fence as a function of the length 'x' of the side that cost $60 per meter.

Homework Equations

A=length*width

The Attempt at a Solution

I have scanned and uploaded my attempt/work onto imgur. here


http://i.imgur.com/SDB9T.jpg


I have attempted the solution, where I had simplified the equation in relation to the cost I am not entirely sure if after that I had solved for the correct variable ( either y or x), and did I input the equation into the right equation (Area of rectangle as a function of length x).

Any help would be greatly appreciated. Is my attempt correct?

*****also, confused when they ask for the area of the lot as a function of the length x. So essentially I only want variable "x" in my area equation?******

You've almost got it. But I don't see why you think l=2x and w=2y? Length is x and width is y.

 

[EIGHTSIX7]

You've almost got it. But I don't see why you think l=2x and w=2y? Length is x and width is y.

What did I do wrong? Can I get a hint? So, I am inputting y=125-1.5x into A= length*w, as w right?

 

[Dick]

What did I do wrong? Can I get a hint? So, I am inputting y=125-1.5x into A= length*w, as w right?

In what you posted you said A=2x*2y. Not A=xy.

 

[EIGHTSIX7]

In what you posted you said A=2x*2y. Not A=xy.

So, aside form my mistake of A= 2x+2y, replaced with A=xy, my answer should be correct?

 

[Dick]

So, aside form my mistake of A= 2x+2y, replaced with A=xy, my answer should be correct?

If you work out A=xy, it should be fine.

 

[EIGHTSIX7]

If you work out A=xy, it should be fine.

Ok, thanks!