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 lease twice as long as she scratched at the corners of her cage, and she spent more than 1/4 hour running on her wheel. Which system of inequalities represents the time zoe kept juile awake last night if x is the number of hours zoe spent running on her wheel and y is the nu=umber of hours spent scratching her cage

Answer 1

Answer: $x+y\geq 1$, $x>\frac{1}{4}$ ,  $x\geq 2y$ and $y\geq 0$

Step-by-step explanation:

Here,  x represents the number of hours Zoe spent running on her wheel and y represents the number of hours spent scratching her cage.

Julie was awoke for at least an hour running on her exercise wheel and scratching the of her cage.

⇒ $x+y\geq 1$

She ran on her wheel at least twice as long as she scratched at the corners of her cage.

⇒ $x\geq 2y$

Also, She spent more than 1/4 hour running on her wheel.

⇒ $x>\frac{1}{4}$

And, we know that number of hours can not be negative.

⇒  $y\geq 0$

Therefore, the complete system of inequality which shows the given situation is,

$x+y\geq 1$, $x>\frac{1}{4}$ and $x\geq 2y$, $y\geq 0$

Note: the feasible region ( covered by the given system) is shown in the below graph.