Question

You have at most 6 hours to spend at a fair and at a planetarium. You want to spend at least 2 hours at the fair and more than 2 hours at the planetarium. Let x be the number of hours at the fair and y be the number of hours at the planetarium. Which system represents the situation

a) x+y≤6 and x≥2 and y>2
b) x+y≥6 and x≥2 and y>2
c) x+y≤6 and x>2 and y≥2
d) x+y≥6 and x>2 and y≥2

Answer 1

The correct system of inequalities that describes spending at most 6 hours between a fair and a planetarium, with at least 2 hours at the fair and more than 2 at the planetarium, is option a) x+y≤6, x≥2, and y>2.

Step-by-step explanation:

The system of inequalities that represents the situation where you have at most 6 hours to spend at a fair and at a planetarium, where you want to spend at least 2 hours at the fair and more than 2 hours at the planetarium is a) x+y≤6 and x≥2 and y>2.

This is because the total time spent at both places cannot exceed 6 hours (x+y≤6), you need to spend 2 or more hours at the fair (x≥2), and more than 2 hours at the planetarium (y>2).