1. **State the problem:** Carlos was given a basketball. We need to find the ratio of tennis balls to baseballs, and the ratio of total balls to tennis balls after adding the basketball. Then compare these ratios before and after adding the basketball. 2. **Original quantities:** - Tennis balls = 4 - Baseballs = 5 - Total balls = 9 (4 tennis + 5 baseball) 3. **Ratios before basketball:** - Tennis balls to baseballs = $\frac{4}{5}$ - Total balls to tennis balls = $\frac{9}{4}$ 4. **After adding basketball:** - New total balls = $9 + 1 = 10$ - Tennis balls = 4 (unchanged) - Baseballs = 5 (unchanged) 5. **Ratios after basketball:** - Tennis balls to baseballs = $\frac{4}{5}$ (unchanged) - Total balls to tennis balls = $\frac{10}{4}$ 6. **Simplify total balls to tennis balls ratio after basketball:** $$\frac{10}{4} = \frac{\cancel{10}}{\cancel{4}} = \frac{5}{2}$$ 7. **Compare ratios:** - Tennis balls to baseballs ratio remains $\frac{4}{5}$ before and after. - Total balls to tennis balls ratio changed from $\frac{9}{4}$ to $\frac{5}{2}$ after adding the basketball. **Final answers:** - Ratio of tennis balls to baseballs: $\frac{4}{5}$ - Ratio of total balls to tennis balls after basketball: $\frac{5}{2}$ The basketball increased the total balls, changing the total-to-tennis ratio but not the tennis-to-baseball ratio.