1. **State the problem:** A vendor sold a total of 224 sodas and hot dogs combined. The number of sodas sold was three times the number of hot dogs sold. 2. **Define variables:** Let $h$ be the number of hot dogs sold and $s$ be the number of sodas sold. 3. **Write equations from the problem:** - Total items sold: $$s + h = 224$$ - Relationship between sodas and hot dogs: $$s = 3h$$ 4. **Substitute the second equation into the first:** $$3h + h = 224$$ 5. **Combine like terms:** $$4h = 224$$ 6. **Solve for $h$:** $$h = \frac{224}{4} = 56$$ 7. **Find $s$ using $s = 3h$:** $$s = 3 \times 56 = 168$$ 8. **Answer:** - Number of sodas sold: 168 - Number of hot dogs sold: 56