To solve this problem, we need to represent the conditions given in the question with a system of inequalities.
1. The park charges [tex]$5 per adult ride and $[/tex]3 per child ride. Thus, the total revenue from adult rides and child rides in 4 years can be expressed as [tex]\(5x + 3y\)[/tex], where [tex]\(x\)[/tex] is the number of adult rides and [tex]\(y\)[/tex] is the number of child rides over the 4 years.
2. The park wants to earn back more than $750,000 for the construction cost. Therefore, the inequality representing this condition is:
[tex]\[ 5x + 3y \geq 750,000 \][/tex]
3. The best weather constraints are that the park can provide at most 100,000 adult rides and 75,000 child rides each season. Over 4 seasons, this translates to:
[tex]\[ x \leq 4 \times 100,000 = 400,000 \][/tex]
[tex]\[ y \leq 4 \times 75,000 = 300,000 \][/tex]
So, the correct system of inequalities that represents this situation is:
[tex]\[
\begin{array}{c}
5x + 3y \geq 750,000 \\
x \leq 400,000 \\
y \leq 300,000 \\
\end{array}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\begin{array}{c}
5x + 3y \geq 750,000 \quad x \leq 400,000 \\
y \leq 300,000
\end{array}
\][/tex]
