SOLUTION: Please help. A rancher has 100 meters of fencing to enclose two adjacent rectangular corrals. 4x + 3y = 100 Write the area A of the enclos

Algebra ->  Formulas -> SOLUTION: Please help. A rancher has 100 meters of fencing to enclose two adjacent rectangular corrals. 4x + 3y = 100 Write the area A of the enclos      Log On


   

Question 122435: Please help.
A rancher has 100 meters of fencing to enclose two adjacent rectangular corrals.
4x + 3y = 100
Write the area A of the enclosed region as a function of x
So far this is what I’ve got-I figured out the function of x and plugged it into the Area formula, but that’s where I get stuck.
P = 100
4x + 3y = 100
4x + 3y – 3y = – 3y + 100
4x+=+%28%26%238211%3B+3y+%2B+100%29%2F4

x+=+-3%2F4y+%2B+25
f%28x%29+=-3%2F4y+%2B+25
A = 2x(y)
A+=%5B+2%28-3%2F4y+%2B+25%29%5Dy
A+=+%28-3%2F2y+%2B+50%29y
A+=+-3%2F2y%5E2+%2B+50y
I know x = 10 and y = 20 works for the perimeter, but don’t know how to write it to show that. When I graph A+=+-3%2F2y%5E2+%2B+50y (making A correspond to y and the y correspond to the x), I don’t get the same area as in the table.
I need to add more values to the table.
X Y Area
2 92/3 368/3 ≈123
4 28 224
Thank you for any help you can give!!!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
4x + 3y = 100 __ subtracting 4x __ 3y=100-4x __ dividing by 3 __ y=(100-4x)/3

A = 2x(y) __ substituting for y __ A=2x(100-4x)/3 __ A=(200x-8x^2)/3

so f(x)=(200x-8x^2)/3