Suppose your income $y$ is directly proportional to the number $x$ of hours you work: $y = cx$, where $c$ is a constant. In addition, suppose you're a big spender and the money $z$ you spend varies with income as $z(y) = a + by^2$, where $a$ and $b$ are also constants. For your income to be larger than your expenses, what conditions on $y$, $a$, and $b$ must be met?
I'm not entirely sure how I am supposed to write the answers(There is no solution on the back of the book). I know that $a < 0$ and $|a/y^2|>b$ but is that how I am supposed to express the conditions? Or am I supposed to express the conditions in terms of $c$ and $x$?