1. **Problem Statement:** We are given data for Fruit A and Fruit B showing the number of fruits purchased, total weight, and total price. We need to determine if the price of Fruit A is proportional to the number of fruits and to the total weight, and then identify which fruit's price depends on the number of fruits and which depends on total weight. 2. **Understanding Proportional Relationships:** A relationship is proportional if the ratio between two quantities is constant. For example, if price and number of fruits are proportional, then \( \frac{\text{price}}{\text{number}} \) is constant. 3. **Check proportionality of Fruit A price to number of fruits:** Calculate \( \frac{\text{price}}{\text{number}} \) for each data point: - For 1 fruit: \( \frac{0.42}{1} = 0.42 \) - For 2 fruits: \( \frac{0.87}{2} = 0.435 \) - For 3 fruits: \( \frac{1.34}{3} \approx 0.447 \) These values are close but not exactly equal, so the relationship is approximately proportional but not perfectly. 4. **Check proportionality of Fruit A price to total weight:** Calculate \( \frac{\text{price}}{\text{weight}} \): - For 4.2 oz: \( \frac{0.42}{4.2} = 0.1 \) - For 8.7 oz: \( \frac{0.87}{8.7} = 0.1 \) - For 13.4 oz: \( \frac{1.34}{13.4} = 0.1 \) This ratio is constant, so price is proportional to total weight. 5. **Analyze Fruit B price relationship:** Look at price vs number of fruits: - 1 fruit: 0.50 - 2 fruits: 1.00 - 3 fruits: 1.50 Price increases exactly by 0.50 per fruit, so price is proportional to number of fruits. Look at price vs total weight: Weights are 2.6, 3.0, 2.9 oz but prices increase steadily. Since weight does not increase steadily, price is not proportional to weight. **Final answers:** - a) The price of Fruit A is nonproportional to the number of fruits (ratios vary slightly) but proportional to total weight. - b) Fruit B's price depends on the number of fruits purchased (proportional), while Fruit A's price depends on total weight (proportional).