You would like to construct a 400-square-foot rectangular garden along your driveway. The fencing on the driveway side costs $15 per linear foot, while the fencing for the other three sides costs $8 per linear foot. Write an expression for the cost of the enclosed rectangular garden as a function of the length L of the garden.
x+3y=400
15x+8*3y=L
15(400-3y)+8*3y+L
Not quite...
The cost C is
C = 8(2W+L)+15L
since LW=400,
= 8(2(400/L)+L) + 15L
= 8(800/L + L) + 15L
= 6400/L + 23L
Thank you Steve :)
To find the cost of the enclosed rectangular garden, we need to calculate the cost of each side separately and then add them up.
Let's start by finding the length and width of the rectangular garden. Since the area is given as 400 square feet, we can set up the equation:
Length (L) * Width (W) = Area (A)
L * W = 400
Now, let's solve for the width (W) in terms of the length (L):
W = 400 / L
Now, we can calculate the cost of each side:
1) The driveway side has a length of L. The cost per linear foot is $15. So, the cost of the driveway side is:
Cost of driveway side = L * Cost per linear foot = 15L
2) The other three sides (two widths and one length) have a total length of 2W + L. The cost per linear foot is $8. So, the cost of the other three sides is:
Cost of other three sides = (2W + L) * Cost per linear foot = 8(2W + L)
Now, let's add up the costs of all four sides to get the total cost of the enclosed rectangular garden as a function of the length L:
Total cost = Cost of driveway side + Cost of other three sides
Total cost = 15L + 8(2W + L)
Since we found W = 400 / L earlier, we can substitute it into the equation:
Total cost = 15L + 8(2 * (400 / L) + L)
Simplify further if needed.