Last night, Julie’s pet hamster Zoe kept Julie awake for at least an hour running on her exercise wheel and scratching at the corner of her cage. Zoe ran on the wheel at least 3 times as long as she scratched at the quarters of her cage, and she spent more than 1/2 hour rubbing on her wheel. Which System of inequalities represents the time Zoe kept Julie awake last night if X is the number of hours that she spent running on her wheel and y is the number of hours spent scratching at her cage?

Question

Last night, Julie’s pet hamster Zoe kept Julie awake for at least an hour running on her exercise wheel and scratching at the corner of her cage. Zoe ran on the wheel at least 3 times as long as she scratched at the quarters of her cage, and she spent more than 1/2 hour rubbing on her wheel. Which System of inequalities represents the time Zoe kept Julie awake last night if X is the number of hours that she spent running on her wheel and y is the number of hours spent scratching at her cage?

Answer 1

Let's analyze the given information step by step.

1. Zoe ran on the wheel at least 3 times as long as she scratched at the quarters of her cage.
This can be represented as:
X ≥ 3y

2. Zoe spent more than 1/2 hour rubbing on her wheel.
This can be represented as:
X > 1/2

Now, let's combine these two inequalities:

X ≥ 3y
X > 1/2

This represents the system of inequalities for the time Zoe kept Julie awake last night.