Toby is packaging 21 baseball cards and 12 football cards to sell at a swap meet. He had determined that it would be best to package them in packets of 3 cards each with 7 packs of baseball cards and 4 packs of football cards. However, Toby then decided to keep one baseball card for himself and sell the rest. How does this change how many packets of each card type there are and how many cards are in each packet? There would be [?] packets of baseball cards and [?] packets of football cards. Each packet would contain [?] cards.

Before, he had 21 baseball cards and 12 football cards.

we know that:

21 = 7*3

12 = 4*3.

He decided to pack the cards in groups of 3, because 3 is the only common factor between 21 and 12.

Now, if he decides to keep one baseball card, now he has:

20 baseball cards and 12 football cards.

Now he has two possibilities for how many cards are in each pack, this is because:

12 = 4*3 = 2*2*3

20 = 4*5 = 2*2*5

12 and 20 have two common factors, 4 and 2.

a) Then he can sell them in packets of 2 cards each with:

12/2 = 6 packs of football.

20/2 = 10 packs of baseball.

b) Or he can sell them in packets of 4 cards each with:

12/4 = 3 packs of football.

20/4 = 5 packs of baseball.

the answer is 8/21

hope this