1. **State the problem:** We have two customers buying cheese and milk. The first customer pays 12.45 dollars for 1 pound of cheese and 2 gallons of milk. The second customer pays 19.70 dollars for 3 pounds of cheese and 1 gallon of milk. We need to find the cost of 1 gallon of milk. 2. **Set variables:** Let $c$ be the cost of 1 pound of cheese and $m$ be the cost of 1 gallon of milk. 3. **Write equations from the problem:** - First customer: $$c + 2m = 12.45$$ - Second customer: $$3c + m = 19.70$$ 4. **Solve the system of equations:** From the first equation, express $c$: $$c = 12.45 - 2m$$ 5. **Substitute $c$ into the second equation:** $$3(12.45 - 2m) + m = 19.70$$ $$37.35 - 6m + m = 19.70$$ $$37.35 - 5m = 19.70$$ 6. **Isolate $m$:** $$-5m = 19.70 - 37.35$$ $$-5m = -17.65$$ 7. **Divide both sides by -5:** $$m = \frac{-17.65}{-5}$$ $$m = \frac{\cancel{-17.65}}{\cancel{-5}} = 3.53$$ 8. **Interpretation:** The cost of 1 gallon of milk is 3.53 dollars. **Final answer:** 3.53 (Option A)