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 twice as long as she scratched at the quarters of her cage, and she spent more than 1/4 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

`x+y\geq 1`

`x\geq 2y`

`x\geq (1)/(4)`

Explanation:

In order to solve this problem, we just need to translate mathematically what the problem is talking about. First, we know that:

x=# of hours she spent running on her wheel.

y = # of hourse she spent scratching at her cage.

So, let's split the problem into little chunks of information that will be easier to translate. This is split it into sentences.

So first:

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. This means that the least amount of time Julie was awake as an hour in total, so this can be written as an inequality like this:

time spent running + time spent scratching is less than or equal to 1 hour

`x+y\geq 1`

next,

Zoe ran on the wheel at least twice as long as she scratched at the quarters of her cage.

This is:

`x\geq 2y`

and finally, she spent more than 1/4 of an hour running on her wheel.

`x\geq (1)/(4)`

so the system of inequalities is the following:

`x+y\geq 1`

`x\geq 2y`

`x\geq (1)/(4)`