Answer
Days $=5$.
People $=234$.
Work Step by Step
Pool A: $y=36x+54$.
Pool B: $y=-x^2+39x+64$
Eliminate $y$
Subtract the two equations.
$\Rightarrow y-y=36x+54-(-x^2+39x+64)$
Clear the parentheses.
$\Rightarrow y-y=36x+54+x^2-39x-64$
Simplify.
$\Rightarrow 0=x^2-3x-10$
Factor and solve.
$\Rightarrow 0=(x-5)(x+2)$
Use the zero product property.
$x-5=0$ or $x+2=0$
Solve for $x$.
$x=5$ or $x=-2$
Eliminate the impossible solution.
Substitute back $x=5$ into the original equation to find the value of $y$.
Pool A:
$\Rightarrow y=36(5)+54$
$\Rightarrow y=180+54$
$\Rightarrow y=234$
Pool B:
$\Rightarrow y=-(5)^2+39(5)+64$
$\Rightarrow y=-25+195+64$
$\Rightarrow y=234$
Hence, the pools had the same attendance on Day $5$ with $234$ people.
