Let's first find the total number of students who decided to buy the gift. Initially, there were 9 students, and then an additional 4 students joined, resulting in a total of 9 + 4 = 13 students.
Next, let's assume that each student initially contributed x dollars toward the cost of the gift.
Since each of the original 9 students saved $33.32, the total savings by the 9 students would be 9 * $33.32 = $299.88.
The total cost of the gift would be the sum of the savings and the amount contributed by the additional 4 students, which is $299.88 + 4x.
Since each student initially contributed the same amount of money, the remaining 4 students would also contribute x dollars each. Therefore, the total amount contributed by the additional 4 students would be 4x.
Setting up an equation, we have:
$299.88 + 4x = 13x
Simplifying the equation, we have:
$299.88 = 9x
Dividing both sides by 9, we find:
x = $33.32
Therefore, each student initially contributed $33.32.
The cost of the gift would be the total savings by the original 9 students plus the contribution from the additional 4 students, which is $299.88 + 4 * $33.32 = $434.48.
Thus, the cost of the gift was $434.48.