1. The problem states that the cost $C$ varies directly with the number of pages $h$ and inversely with the number of copies $n$. This means we can write the formula as: $$C = k \frac{h}{n}$$ where $k$ is a constant of proportionality. 2. We are given that when $h = 100$ pages and $n = 200$ copies, the cost $C = 2000$. Substitute these values to find $k$: $$2000 = k \frac{100}{200}$$ Simplify the fraction: $$2000 = k \times \frac{1}{2}$$ Multiply both sides by 2 to solve for $k$: $$2 \times 2000 = \cancel{2} \times k \times \frac{1}{\cancel{2}}$$ $$4000 = k$$ 3. Now express $C$ in terms of $h$ and $n$ using the value of $k$: $$C = 4000 \frac{h}{n}$$ This answers part (a). 4. For part (b), find the cost to produce 500 copies each with 150 pages: $$C = 4000 \frac{150}{500}$$ Simplify the fraction: $$C = 4000 \times \frac{3}{10}$$ Calculate the cost: $$C = 1200$$ So, the cost to produce 500 copies with 150 pages each is 1200. **Final answers:** (a) $$C = 4000 \frac{h}{n}$$ (b) $$C = 1200$$