Final answer:
The minimum number of each card type that the store must have sold is 10 thank-you cards and 5 birthday cards.
Step-by-step explanation:
To determine the minimum number of each card type that the store must have sold, we need to find the common factors of 10 and 5. These common factors represent the possible numbers of packs that the store could have sold for both thank-you cards and birthday cards.
The common factors of 10 and 5 are 1 and 5. Therefore, the minimum number of packs the store must have sold is 1.
Since each pack contains 10 thank-you cards and 5 birthday cards, the minimum number of thank-you cards sold is 1 pack x 10 cards = 10 cards.
Similarly, the minimum number of birthday cards sold is 1 pack x 5 cards = 5 cards.