Part A:
Given that Rachel is planning a wedding for 100 to 250 people, the inequality in terms of p people that describes how many people Rachel plans to invite is given by:
100 ≤ p ≤ 250
Part B:
Given that the caterer charges $20 per person, plus a flat fee of $200, the inequality that shows how much the caterer will charge in terms of p is given by:
20(100) + 200 ≤ 20p + 200 ≤ 20(250) + 200
Part C:
The range of catering fees (C) that Rachel is considering is given by:
20(100) + 200 ≤ 20p + 200 ≤ 20(250) + 200
2000 + 200 ≤ C ≤ 5000 + 200
2200 ≤ C ≤ 5200
Therefore, the range of catering fees Racheal is considering is from $2,200 to $5,200
