Quadratic Word Problem: Pool Problem

Question

Steps to take:
1. Draw diagrams
2. Decide what X will stand for
3. Write an equation that uses the variable and the info they give you
4. Set the equation equal to zero
5. Factor
6. Solve

 

Word Problem: You are building a pool area that consists of a rectangular swimming pool and a concrete walkway of even width surrounding all four sides of the pool. The entire pool area has a total of 15,000 square feet. The pool itself is 120 ft. by 70 ft. Find the width of the walkway.

Answer 1

x will represent the width of the walkway

so the concrete area will be bigger than 120x70.  The concrete pool will have 120+x+x as its length because there is x feet on each side.  120+2x.  Similarly the width of the pool will be 70+x+x for the same reason or 70+2x.

 

OK, so now the area of concrete will be the LxW or (120+2x)(70+2x)= area=15000

 

All that's left is to FOIL and solve the quadratic equation.  Or if you have a graphing calculator, you can use that to find the intersection points.  Expect two solutions but one might be negative and not make sense to the physical problem.