A children'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.

Let x be the number of children who can attend the birthday party.

The inequality for the number of children who can attend the birthday party is:
6.25x + 50 ≤ 100

Subtract 50 from both sides of the inequality:
6.25x ≤ 50

Divide both sides of the inequality by 6.25:
x ≤ 8

Therefore, Gina can invite no more than 8 children to her son's fourth birthday party.