Question

Kayla has $500 in her account, and she spends $40 a week on food. If she falls below $30 in her account, she must pay a penalty. What is an inequality that can represent this situation?

Answer 1

She starts with $500; that's a given. If she's spending $40 a week, that means that she'll be subtracting $40 from her account for each week (let's call the number of weeks that've gone by "w"), leaving her with 500-40w dollars after week w.

Now we have to compare this somehow to $30. Our inequality is going to look like:

500-40w ? 30

Where the ? is a stand-in for an inequality sign. Which inequality sign should we pick? Take a look at the question and see if you can find any keywords that might give you a hint. "If she falls below" is the big one I'm seeing. If she can't fall below $30, that means she'll always have to stay at or above $30 to avoid paying the penalty. What inequality sign represents at or above?