Achildren's birthday party at an indoor play center costs $50 to rent the space and $6.25 per child. gina wants to spend no more than $100 on her son's 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 ≥ 100; x ≥ 8 c) 50 + 6.25x < 100; x < 8 d) 50 + 6.25x > 100; x > 8

The key idea is what to do with the eight. If she is willing to spend 100 dollars and the cost of the hall is 50 dollars she is left with 100 - 50 = 50 dollars.
Since is willing to spend no more than 100 then she can spend exactly 100.

B is wrong, there is no way x can have a value over 100 dollars.
C is wrong. She can spend exactly 100 dollars.
D is wrong. There is no way she will go over 100 dollars.

That leaves A. That is correct. She can spend exactly 100 and there are 8 children max that can attend -- exactly what the answer requires.