Homework Help: Math

Posted by Vic on Monday, November 19, 2012 at 8:46pm.

Jennifer plans to fence a rectangular area around her rectangular swimming pool. The total area enclosed by the fence, including the pool, should be 5 times the area of the pool alone. The pool is 20 feet by 17 feet.
A.)What is the total area enclosed by the fence?

B.) fencing costs $8 per linear foot. Jennifer plans to build the fence so that the length of the fence will be 25 feet on the 20 foot side of the pool. What is the cost of the fencing with this plan?

C.) Jennifer decides that the cost of her original plan is to expensive. She wants to find the dimensions of the fence with the least cost. What is a formula, C(w), for the cost of the fence if the length of the fence is w feet on the 20 foot side of the pool?

Math - Vic, Monday, November 19, 2012 at 11:03pm
Please Some help me with this problem!!!!!!!!!!!!!!!!!!!!!
Math - Steve, Tuesday, November 20, 2012 at 12:18am
just start by translating the facts into symbols.

(A)
the pool is 20 by 17, so its area is 340.
The total area will be 5 times that, or 1700.

(B)
the fence is 25 feet long, so its width is 1700/25 = 68 ft. The perimeter is thus 2(25+68) = 186 ft. At $8/ft that will cost $1488.

(C)
from (B) we know the cost is 8*2(w+1700/w).
C(w) = 16w + 27200/w

Don't know why it keeps mentioning the side along the length of the pool. All we care about is the fence, not its relationship to the pool.

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