While traveling for vacation, you have decided to divide your lodging between a resort and a regular stay hotel. Let x represent the number of nights you will spend in a resort and let y represent the number of nights you will spend in a regular stay hotel.

A) Write a system of inequalities that models the following conditions:
1) You want to stay at least 5 nights
2) At least one night will be spent at a resort
3) Resorts average $200 per night and regular stay hotels average $100 per night. Your budget does not exceed $700 for lodging
B) How do I graph the solution set of my system of inequalities?
C) How many nights can you spend at resort and stay within your budget?
Please help me with all of these questions!!

A) To model the given conditions, we need to write a system of inequalities. Let's analyze each condition separately:

1) You want to stay at least 5 nights
This condition can be written as:
x + y ≥ 5

2) At least one night will be spent at a resort
This condition can be written as:
x ≥ 1

3) Your budget does not exceed $700 for lodging
This condition can be written in terms of the cost per night at the resort (200x) and at the regular stay hotel (100y) as:
200x + 100y ≤ 700

Therefore, the system of inequalities that models the given conditions is:
x + y ≥ 5
x ≥ 1
200x + 100y ≤ 700

B) To graph the solution set of the system of inequalities, follow these steps:
1) Graph the line x + y = 5 by finding two points that lie on this line. For example, you can use (0, 5) and (5, 0). Draw a dashed line through these points.

2) Graph the line x = 1 by drawing a vertical line passing through x = 1. This line should be solid.

3) Graph the line 200x + 100y = 700 by finding two points that lie on this line. For example, you can use (3.5, 0) and (0, 7). Draw a dashed line through these points.

4) Shade the region of the graph that satisfies all three inequalities. The shaded region should be above or on the line x + y = 5, to the right or on the line x = 1, and below or on the line 200x + 100y = 700. The shaded region represents the solution set.

C) To determine how many nights you can spend at the resort and stay within your budget, locate the intersection point(s) of the line 200x + 100y = 700 with the other two lines in the graph. The x-coordinate of this intersection point(s) will give you the number of nights you can spend at the resort while staying within your budget.