A ship departs from Port Miami with 5,678 tons of cargo. The ship docks at the Bahamas and unloads some cargo. The crew also loads three times the quantity of cargo that was unloaded. If the ship holds 8,588 tons now, how many tons of cargo did the ship unload at the Bahamas?

Answer 1

Let \( x \) be the amount of cargo unloaded at the Bahamas.

When the ship unloads \( x \) tons of cargo, the remaining cargo on the ship is:

\[ 5678 - x \]

Then, the crew loads three times the amount of cargo that was unloaded, which is:

\[ 3x \]

After loading this cargo, the total cargo on the ship becomes:

\[ (5678 - x) + 3x = 5678 + 2x \]

According to the problem, after these transactions, the total cargo on the ship is 8588 tons. Therefore, we can set up the following equation:

\[ 5678 + 2x = 8588 \]

Now, we will solve for \( x \) by first isolating \( 2x \):

\[ 2x = 8588 - 5678 \]

Calculating the right side:

\[ 2x = 2910 \]

Now, divide both sides by 2 to solve for \( x \):

\[ x = \frac{2910}{2} = 1455 \]

Thus, the amount of cargo that the ship unloaded at the Bahamas is:

\[ \boxed{1455} \text{ tons} \]