SOLUTION: A rectangular tract of land 40 feet by 46 feet is to have a rectangular swimming pool built in the middle of it. The pool is to occupy 60% of the area of the tract. The edges of th

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A rectangular tract of land 40 feet by 46 feet is to have a rectangular swimming pool built in the middle of it. The pool is to occupy 60% of the area of the tract. The edges of th      Log On


   

Question 867045: A rectangular tract of land 40 feet by 46 feet is to have a rectangular swimming pool built in the middle of it. The pool is to occupy 60% of the area of the tract. The edges of the pool area are to be the same distance from the edges of the tract. What are the dimensions of the pool?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The constant but unknown variable, w, is the distance described as , "The edges of the pool area are to be the same distance from the edges of the tract." That is for the non-pool area.

Area of land tract plus pool: 40%2A46.
Area of base of pool: %2840-2w%29%2846-2w%29.
A ratio of areas is given, pool/LandTract: highlight_green%28%2840-2w%29%2846-2w%29%2F%2840%2A46%29=0.6%29

PROCESS:
(1) Find the value of w.
(2) Use w to find the dimensions, (40-2w) and (46-2w).


Nothing more on this solution post unless you find the process does not work or you find trouble within it.
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Further explanation will help.
According to the problem description, the area (40-2w)(46-2w) is 60% of the area 40*46. The green highlighted equation comes from this description. First goal then, is to solve for w from that equation.