SOLUTION: You want to enclose a rectangular lot with fencing. One side of the lot runs along the highway. The fencing along the highway costs $10 per foot and the rest of the fencing costs $

Algebra ->  Functions -> SOLUTION: You want to enclose a rectangular lot with fencing. One side of the lot runs along the highway. The fencing along the highway costs $10 per foot and the rest of the fencing costs $      Log On


   

Question 172882: You want to enclose a rectangular lot with fencing. One side of the lot runs along the highway. The fencing along the highway costs $10 per foot and the rest of the fencing costs $7 a foot. The total money available for fencing is $6,000. The cost equation for the fencing is 7(2W+L)+10L = 6000, where L is the length of the lot and W is the width of the lot. The area of the lot, A, is given by the formula A=LW.
Can you step me through the following:
1. By writing the width as a function of the length, find the width of the lot, if its length is 100 feet (Width = ).
2. Write the area of the lot as a function of the length (A(L) = ).
3. What will be the area of the lot if the length is 100 feet (Area = )?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You want to enclose a rectangular lot with fencing. One side of the lot runs along the highway. The fencing along the highway costs $10 per foot and the rest of the fencing costs $7 a foot. The total money available for fencing is $6,000. The cost equation for the fencing is 7(2W+L)+10L = 6000, where L is the length of the lot and W is the width of the lot. The area of the lot, A, is given by the formula A=LW.
:
Can you step me through the following:
;
1. By writing the width as a function of the length, find the width of the lot, if its length is 100 feet (Width = ).
:
Take the original equation, rearrange to find W:
7(2W+L)+10L = 6000,
14W + 7L + 10L = 6000
14W + 17L = 6000
14W = 6000 - 17L
W = %28%286000-17L%29%29%2F14
:
L = 100'
W = %28%286000-17%28100%29%29%29%2F14
W = %28%286000-1700%29%29%2F14
W = 4300%2F14
W = 307.14'
:
:
2. Write the area of the lot as a function of the length (A(L) = ).
:
from the above we have W as the function L;
Substitute, %28%286000-17L%29%29%2F14 for W in the A=L*W
A = L*(%28%286000-17L%29%29%2F14)
:
:
3. What will be the area of the lot if the length is 100 feet (Area = )?
:
Substitute 100 for L in the above equation:
A = L*(%28%286000-17L%29%29%2F14)
A = 100*(%28%286000-17%28100%29%29%29%2F14)
A = 10*(%28%286000-1700%29%29%2F14)
A = 100 * 307.14
A = 30714 sq ft