Given the sketch of the pool:
The total area of the Adult pool is:
[tex]A=15000\text{ ft}^2[/tex]
According to the sketch, this is equivalent to:
[tex](120+2x)(70+2x)=15000[/tex]
Solving for x (the width of the walkway):
[tex]\begin{gathered} 120\cdot70+120\cdot2x+70\cdot2x+4x^2=15000 \\ 8400+380x+4x^2=15000 \\ 4x^2+380x-6600=0 \\ \\ \Rightarrow x^2+95x-1650=0 \end{gathered}[/tex]
This is equivalent to:
[tex]\begin{gathered} x^2+95x-1650=(x+110)(x-15)=0 \\ \\ \Rightarrow x+110=0\Rightarrow x=-110\text{ \lparen Incorrect, the width must be positive\rparen} \\ \Rightarrow x-15=0\Rightarrow x=15\text{ ft \lparen Correct answer\rparen} \end{gathered}[/tex]
