3) 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.

Question

a. Write a system of inequalities that models the following conditions:
i. You want to stay at least 5 nights
ii. At least one night will be spent at a resort
iii. Resorts average $200 per night and regular stay hotels average $100 per night. Your budget does not exceed $700 for lodging.
b. Graph the solution set of your system of inequalities
c. Based on your graph, how many nights can you spend at a resort and stay within your budget?

Answer 1

1. x + y > 5

2. x > 1

3. 200x + 100y < 700

Cannot graph here.