1. **State the problem:** You sold hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. The total money made is 78.50, and the total number of items sold (hot dogs + sodas) is 87. We need to find how many hot dogs were sold. 2. **Define variables:** Let $h$ be the number of hot dogs sold and $s$ be the number of sodas sold. 3. **Write the system of equations:** $$h + s = 87$$ $$1.5h + 0.5s = 78.5$$ 4. **Solve the system:** From the first equation, express $s$ in terms of $h$: $$s = 87 - h$$ 5. Substitute $s$ into the second equation: $$1.5h + 0.5(87 - h) = 78.5$$ 6. Distribute and simplify: $$1.5h + 0.5 \times 87 - 0.5h = 78.5$$ $$1.5h + 43.5 - 0.5h = 78.5$$ 7. Combine like terms: $$ (1.5h - 0.5h) + 43.5 = 78.5$$ $$1.0h + 43.5 = 78.5$$ 8. Subtract 43.5 from both sides: $$h = 78.5 - 43.5$$ $$h = 35$$ 9. **Answer:** You sold **35 hot dogs**.