A jug can hold 6 liters of water and a mug can hold 2 liters. A bottle contains 20 liters. What is the minimum number of jugs and mugs required to fill the bottle exactly? Give the numbers of jugs and mugs.

Step-by-step solution

1. Write the equation $6j+2m=20$ where $j$ is the number of jugs and $m$ the number of mugs.
2. Divide both sides by 2 to simplify: $3j+m=10$.
3. To minimise $j+m$ use the largest possible $j$ that keeps $m$ non‑negative.
4. Try $j=3$: then $m=10-3\times 3=1$ (total 4 containers).
5. Check smaller $j$: $j=2$ gives $m=4$ (6 containers); $j=1$ gives $m=7$ (8 containers).
6. Thus the minimum occurs at $j=3$, $m=1$.

Concept tested: minimum containers with two capacities

Published 7 October 2026 · How this solution was prepared and checked