"The Book Palace" exhibits a proportional relationship between time and books sold, with a consistent ratio of 3 books per day. In contrast, "Discount Books" lacks a constant ratio, indicating a non-proportional relationship.
To determine if there is a proportional relationship between time and books sold, we need to check if the ratio of books sold to time is constant.
For "The Book Palace":
- Day 1: \( \frac{3}{1} = 3 \)
- Day 2: \( \frac{6}{2} = 3 \)
- Day 3: \( \frac{9}{3} = 3 \)
For "Discount Books":
- Day 1: \( \frac{1}{1} = 1 \)
- Day 2: \( \frac{4}{2} = 2 \)
- Day 3: \( \frac{5}{3} \approx 1.67 \)
The Book Palace maintains a constant ratio of 3 books per day, indicating a proportional relationship. In contrast, Discount Books does not have a constant ratio, so it does not represent a proportional relationship between time and books. Therefore, "The Book Palace" sale represents a proportional relationship.