SOLUTION: Suppose you have an outdoor pool measuring 25ft. by 10ft. You want to add a cement walkway around the pool. If the walkway will be 1 ft. thick and you have 304ft^3 (cubed) of cemen

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Suppose you have an outdoor pool measuring 25ft. by 10ft. You want to add a cement walkway around the pool. If the walkway will be 1 ft. thick and you have 304ft^3 (cubed) of cemen      Log On


   

Question 1008345: Suppose you have an outdoor pool measuring 25ft. by 10ft. You want to add a cement walkway around the pool. If the walkway will be 1 ft. thick and you have 304ft^3 (cubed) of cement, how wide should the walkway be?
Please explain it step by step because I have a test Monday and I don't understand this concept.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
This cement walkway is a three-dimensional rectangular frame. Your 1 foot thickness is for the up-down direction, and you have unknown uniform width. The question asks for this uniform width.

Analyze the description.
Let u be the uniform width of the pathway or walkway around the pool.
Inner area for the pool, 25%2A10 square feet;
Outer area of the frame or walkway PLUS pool, %2825%2B2u%29%2810%2B2u%29;
The TOP or the BOTTOM area for the walkway is %2825%2B2u%29%2810%2B2u%29-25%2A10;

Use the next two facts:
height or up&down thickness is 1 foot, and the volume for the walkway must be 304 cubic feet.

Walkway base area multiplied by 1 foot thickness is the 304 cubic foot of volume.
highlight%28%28%2825%2B2u%29%2810%2B2u%29-25%2A10%29%2A1=304%29.
Simplify this, and once in a comfortable general quadratic equation form, solve for u.

I leave this solution to the extent shown, not finished and you just need to do those arithmetic or algebra steps.