Final answer:
Jessica initially brought with her 108 grapes.
Step-by-step explanation:
To solve this problem, we can work backwards. If Jessica has 16 grapes left after giving away a third, four, and then half, we can think about how many grapes she had before each step.
Starting with 16 grapes left, we know that this is half of what she had after giving away half. So, if she had 2 times as many grapes after giving away half, then she had 32 grapes before giving away half.
Next, we know that she gave 4 grapes to Monica, so before that, she had 32 + 4 = 36 grapes. Finally, before giving away a third, she must have had three times as many grapes, or 36 x 3 = 108 grapes.
Therefore, Jessica initially brought with her 108 grapes.