SOLUTION: I can't seem to solve this problem that should be easy. I'm blocked and need to figure out how to solve it. A person is building a storage area with 10 short walls of x length

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Question 136441: I can't seem to solve this problem that should be easy. I'm blocked and need to figure out how to solve it.
A person is building a storage area with 10 short walls of x length and 2 long walls of y length. (This looks like a long row of rectangles with y being the total length of all of them together) The total wall length will be 500ft.
For the first part of the problem I was supposed to find a formula for area in terms of x so I used A=xy which turned into x=A/y
Then I set up the equation to start finding then lengths of x and y. So I set up 10x + 2y = 500 and solved for x which is x=50 - 1/5y
So what now? I have a complete mental block and need to know where to go or what I have done wrong to get myself confused up to now. Thanks.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You now have two equations and three unknowns. You can't solve that for specific values of x and y. You CAN find the graph. With the graph, you can easily find values for x and y once you are given some additional information.
Given:A=xy and x+=+%28500+-+2y%29%2F10
A+=+%28%28500-2y%29%2Ay%29%2F10
10A+=+500y+-+2y%5E2
5A+=+100y+-+y%5E2
A+=+20y+-+%28y%5E2%29%2F5

Let's assume the person wants to get the maximum area
Plot the parabola to find the max value of A OR use derivatives to find the f` OR set A equal to 0 and find the two y values that are solutions. Then use that to find the line of symmetry and get the vertex.