1. **State the problem:** We want to buy equal numbers of two types of items costing 7 and 10 each, with a total budget of 300. We need to find the maximum number of items we can buy. 2. **Define variables:** Let $x$ be the number of each type of item bought. Since the numbers are equal, total items bought is $2x$. 3. **Write the cost equation:** Total cost is $7x + 10x = 17x$. 4. **Apply the budget constraint:** The total cost must be less than or equal to 300, so: $$17x \leq 300$$ 5. **Solve for $x$:** $$x \leq \frac{300}{17} \approx 17.65$$ Since $x$ must be an integer, the maximum $x$ is 17. 6. **Calculate total items:** Total items = $2x = 2 \times 17 = 34$. **Final answer:** The maximum number of items that can be bought, with equal numbers of both types, is **34**.