Final answer:
Pirate Jack's entire treasure was $18,000. This was calculated by determining that Pirate Joe's share of $3,000 represented 1/3 of the remaining treasure after half was buried, which meant the remaining was $9,000 and the total treasure was twice this amount.
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with fraction operations. Pirate Jack originally buried a certain amount of treasure. After that, he gave 1/3 of the remaining treasure to Pirate Joe, who received $3,000 in gold. To find the original amount Jack had, we assume the remaining amount after burying some was 'x'. After giving 1/3 to Joe, which equates to $3,000, we can write the equation as (1/3)x = $3,000. Solving for 'x' gives us x = $3,000 * 3, which is $9,000. Since this $9,000 represents the amount Jack was left with after burying 1/2 of his total treasure, we can then find the initial total by multiplying $9,000 by 2, resulting in a total of $18,000. Thus, Pirate Jack's whole treasure was $18,000.