Question

1. a childrens birthday party at an online play center costs $50 to rent the space and $6.25 per child. gina wants to spend no more than $100 on her sons fourth birthday party. write an inequality for the number of children who can attend the birthday party, and solve the inequality. a \\( 50 + 6.25x = 100; x = 8 \\) b \\( 50 + 6.25x \leq 100; x \leq 8 \\) c \\( 50 + 6.25x \geq 100; x \geq 8 \\) d \\( 50 + 6.25x > 100; x > 8 \\)

Explanation:

Step1: Define variable

Let $x$ = number of children.

Step2: Set up total cost

Fixed cost: $\$50$, variable cost: $\$8.25x$. Total cost: $50 + 8.25x$.

Step3: Apply spending limit

Total cost ≤ $\$100$, so $50 + 8.25x \leq 100$.

Step4: Solve for $x$

Subtract 50: $8.25x \leq 50$
Divide by 8.25: $x \leq \frac{50}{8.25} \approx 6.06$
Round down (whole children): $x \leq 6$

Answer:

B. $50 + 8.25x \leq 100; x \leq 6$