Question

Toby is packaging 21 baseball cards and 12 football cards to sell at the swap meet. Each packet will have the same number of cards. Each packet will have the cards for only one sport. What is the greatest number of cards you can place each packet? How many packets would it be for each sport?

Answer 1

Answer: The greatest number of cards you can place each packet = 3

There would be 7 packets of baseball cards and 4 packets of football cards.

Explanation:

Given: Number of baseball cards =21

Number of football cards = 12

Each packet will have the same number of cards.

Each packet will have the cards for only one sport.

Then, the greatest number of cards you can place each packet = GCD (21,12) i.e. greatest common divisor of 21 and 12

Since 21 = 3 x 7 and 12 = 2 x2 x3

so, GCD(21, 12)=3

So, the greatest number of cards you can place each packet = 3

Number packets of baseball cards =
`(21)/(3)=7`

Number packets of football cards =
`(12)/(3)=4`

So, there would be 7 packets of baseball cards and 4 packets of football cards.