grade (5) math

Design a rectangular dog pen that has the greatest possible area and keep within a budget of $50. Your pen needs at least one gate for your dog. Fencing is $1.00 per foot, fence posts are $2.00 each, and gates(3 feet wide) are $5.00 each. What is the area of a pen?
pls help me!!!

asked by ary
  1. If the pen has dimensions x and y, with n gates, and assuming there are posts only at the corners and on both sides of the gate(s) and that the gate(s) do not share a corner post, then using up the whole budget,

    (2x+2y-3n)+2(4+2n)+5n = 50
    x+y+3n = 25
    and, since the gates are 3' wide,
    x > 3
    y > 3

    More gates mean less budget for fence, so go with one gate

    That gives x+y=22 and since the maximum area for a given perimeter is a square, the dog pen will be

    11 by 11, with one gate.

    Cost for 39 feet of fence, one gate, and 6 posts is 39+5+12=50

    posted by Steve
  2. thsnku so much steve!!

    posted by ary
  3. Pls still I don't understand how u got 25 could u pls tell me than tell me what is the area of the rectangle dog pen?
    Pls help me

    posted by Art
  4. Above 39+5+12=56.

    Correct size is 9x9.
    9+9+9+6=33ft fence= $33
    6 posts = $12
    1 gate = $ 5
    ---
    $50

    posted by Marko

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