1. The problem is to understand and analyze the formula for $N$ given by $$N = \frac{6000}{5p + z}.$$\n\n2. This formula expresses $N$ as a function of two variables $p$ and $z$. The numerator is a constant 6000, and the denominator is a linear expression $5p + z$.\n\n3. Important rules:\n- Division by zero is undefined, so $5p + z \neq 0$.\n- As $5p + z$ increases, $N$ decreases, and vice versa, because $N$ is inversely proportional to $5p + z$.\n\n4. To simplify or evaluate $N$ for given values of $p$ and $z$, substitute those values into the denominator and compute the fraction.\n\n5. Example: If $p=2$ and $z=10$, then $$5p + z = 5 \times 2 + 10 = 10 + 10 = 20.$$\nSo, $$N = \frac{6000}{20} = 300.$$\n\n6. If you want to isolate $p$ or $z$, you can rearrange the formula. For example, to solve for $p$:\n$$N = \frac{6000}{5p + z} \implies 5p + z = \frac{6000}{N}.$$\nThen, $$5p = \frac{6000}{N} - z,$$\nand $$p = \frac{\frac{6000}{N} - z}{5}.$$\n\n7. When simplifying fractions or expressions, if any common factors appear, you can cancel them using \cancel{} notation, but here the expression is already simplified.