A jug can hold 3 liters and a mug can hold 1 liter. A bottle holds 14 liters. What is the minimum number of jugs and mugs needed to fill the bottle exactly?

Step-by-step solution

1. Let $j$ be the number of jugs and $m$ the number of mugs.
2. Write the volume equation: $3j+1m=14$.
3. Find integer solutions that minimize $j+m$.
4. Take the maximum possible jugs: j_{max} = leftlfloor\frac{14}{3}\right\rfloor = 4, giving a remainder of 2, so $m=2$.
5. Check other possibilities: $j=3,m=5$ gives 8 containers; $j=2,m=8$ gives 10; $j=1,m=11$ gives 12; $j=0,m=14$ gives 14.
6. The smallest total $j+m$ is 6, achieved with $j=4$ and $m=2$.
7. Therefore the minimum number of containers is 6.

Concept tested: Least number of containers

Published 1 October 2026 · How this solution was prepared and checked