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 $
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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) (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 =
:
L = 100'
W =
W =
W =
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, for W in the A=L*W
A = L*()
:
:
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*()
A = 100*()
A = 10*()
A = 100 * 307.14
A = 30714 sq ft
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