A cargo ship starts with some unknown number of containers. At the first port it drops two thirds of its cargo and then loads 60 more containers. At the second port it again drops two thirds of this cargo and then loads 11 more containers. On reaching the third port, it has exactly 48 containers on board. How many containers were on the ship at the start?

Introduction / Context:

This word problem tests your skill with linear equations and percentage style reductions in a real world setting. A cargo ship repeatedly drops two thirds of its load and then takes on a fixed number of containers at each port. You must carefully model these operations using algebra in order to determine the original number of containers on board before any stops.

Given Data / Assumptions:

• Let the initial number of containers be N.
• At the first port, the ship drops two thirds of its cargo and takes 60 more containers.
• At the second port, the ship drops two thirds of its current cargo and then takes 11 more containers.
• At the third port, the final number of containers is 48.
• We assume all container counts are whole numbers.

Concept / Approach:

We represent each operation algebraically. Dropping two thirds of the cargo means keeping one third of the containers. Loading a fixed number of containers is modelled by addition. We apply these operations step by step starting from N. After two such stages, we set the resulting expression equal to 48 and solve the resulting linear equation in N.

Step-by-Step Solution:

Verification / Alternative check:

Check the process with N = 153. After the first port, keeping one third gives 153 / 3 = 51 containers, then the ship loads 60, reaching 111. At the second port, it keeps one third of 111, which is 37, and then loads 11 more to reach 48. This matches the final condition in the question, confirming N = 153 is correct.

Why Other Options Are Wrong:

Substituting 189, 159, 161, or 171 as the starting number and repeating the described operations will not lead to exactly 48 containers at the final port. Each incorrect value either yields a non integer count at some step or a final count different from 48.

Common Pitfalls:

A common error is to remove one third instead of two thirds, or to misinterpret the phrase "drops two thirds" as keeping two thirds. Another typical mistake is to apply the two operations at each port in the wrong order, loading first and then dropping two thirds. Carefully translating the language into algebraic steps is essential.

Final Answer:

The ship originally carried 153 containers.