Final answer:
Vincent had 102 original Pokemon cards; after receiving 48 as a gift and losing one-third to his dog, he was left with 100 cards. Therefore, before the gift, it was 102 cards, and after the gift, 150 cards in total, making option B the correct answer.
Step-by-step explanation:
To determine how many cards were in Vincent's original collection, we need to perform a little bit of reverse arithmetic. If Vincent ends up with 100 cards after losing one-third of his collection, that means he has two-thirds of his collection remaining. If two-thirds of the collection is 100 cards, then each third is equal to 100 divided by 2, which is 50 cards. The whole collection is therefore 3 times 50, which is 150 cards. However, we must remember that he received an additional 48 cards for his birthday. This means that prior to the birthday gift, he had 150 - 48 cards. So, the original number of cards was 102.
Using this information, we can choose the correct answer:
- A. 120 cards
- B. 150 cards
- C. 144 cards
- D. 1200 cards
In conclusion, the original collection consisted of 102 cards plus the 48 cards he received as a gift for a total of 150 cards. Therefore, the correct answer is B. 150 cards.